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Related Videos

Limit of a Rational Function

Finding the limit of a rational function algebraically

Vertical Asymptotes and Holes of a Rational Function

Finding the holes and vertical asymptotes of a rational function

Limit at Negative Infinity of a Rational Function

Solving a limit approaching negative infinity for a rational function

Limits at Infinity of a Rational Function

Solving the limits approaching infinity and negative infinity of a rational function

Limits at Infinity of a Rational Function 2

Solving the limits approaching infinity and negative infinity of a rational function

Evaluating Limits from a Graph

Finding limits from the graph of a piecewise function

Evaluating One-Sided Limits from a Graph

Finding one-sided limits from the graph of a piecewise function

Evaluating a Limit Numerically

Finding the limit of a function numerically using a calculator

Combinations of Limits from Graphs

Finding limits of combinations of functions using their graphs

Evaluating Limits Algebraically

Using the properties of limits to find several limits algebraically

Limit of a Piecewise Function

Finding one and two-sided limits for a piecewise function algebraically

Limit with Multiple Fractions

Finding the limit algebraically of a function with multiple fractions

Limit of a Fraction with a Square Root

Finding the limit algebraically of a function with a square root in the numerator of a fraction

Limit with an Absolute Value

Finding the limit algebraically of a function with an absolute value

Horizontal Asymptote of a Fraction with Exponential Functions

Finding the horizontal asymptotes of a function that is a fraction with exponentials in the numerator and denominator

Limits at Infinity of a Fraction with Exponential Functions

Solving the limits approaching infinity and negative infinity with exponential functions in the numerator and denominator

Where the Graph of a Function is Not Continuous

Determining where a piecewise function is continuous from its graph

Instantaneous Rate of Change of a Rational Function

Finding the exact value of the instantaneous rate of change

Finding the Derivative of a Rational Function Using the Limit Definition

Using the limit definition to find the derivative of a rational function

Finding a Derivative by Simplifying a Rational

Finding the derivative of a rational function by simplifying and using the power rule

Finding Where a Function is Increasing and Decreasing

Determining the intervals where a function is increasing and decreasing

Using the Quotient Rule Twice to Find the Second Derivative

Using the quotient rule twice to find the second derivative of a rational function

Absolute Extrema on a Closed Interval

Finding the absolute maximum and minimum of a rational function on two closed intervals

Review for the Common Exam: MATH 151 Exam 1 Review Problems 14-25

Review of limits, continuity, and the Intermediate Value Theorem

Review for the Common Exam: MATH 151 Exam 1 Review Problems 26-35

Review of the limit definition of a derivative and calculating the derivative

Review for the Common Exam: MATH 151 Exam 3 Review Problems 8-15

Review of limits and derivatives of inverse trigonometric functions

Review for the Common Exam: MATH 151 Exam 1 Review Problems 26-35

Review of the limit definition of a derivative and calculating the derivative

Review for the Common Exam: MATH 151 Exam 3 Review Problems 8-15

Review of limits and derivatives of inverse trigonometric functions

Limits: MATH 151 Problems 6-20

Evaluating limits of functions

Limits: MATH 151 Problems 6-20

Evaluating Limits of Functions

Continuity: MATH 151 2.5 Problems 1-6

Continuity of Functions and the Intermediate Value Theorem

Limits and Asymptotes: MATH 151 2.6 Problems 7-11

Limits at infinity and asymptotes, along with physics applications

Limits and Asymptotes: MATH 151 2.7 Problems 7-11

Limits at infinity, asymptotes, and tangent lines

Review for the Common Exam: MATH 151 3.1 Exam 1 Review Problems 26-35

Review of the limit definition of a derivative and calculating the derivative

Review for the Common Exam: MATH 151 3.2 Exam 1 Review Problems 26-35

Review of the limit definition of a derivative and calculating the derivative

Riemann Sums and Definite Integrals: MATH 151 5.2 Problems 6-12

Using Reimann sums and the Fundamental Theorem of Calculus

Riemann Sums and Definite Integrals: MATH 151 5.3 Problems 6-12

Using Riemann sums and the Fundamental Theorem of Calculus

MLC WIR 20B M151 week3 #16

Finding the vertical and horizontal asymptotes for a rational function

MLC WIR 20B M151 week7 #4a

Evaluating a limit using L'Hospital's Rule

MLC WIR 20B M151 week9 #8a

Evaluating a limit using logarithm properties

MLC WIR 20B M151 week9 #8b

Evaluating a limit with an indeterminate difference using a common denominator

MLC WIR 20B M151 week10 #6a

Evaluating a a limit from the left for a rational function

MLC WIR 20B M151 week10 #6b

Evaluating the limit of a rational function by factoring and cancelling

MLC WIR 20B M151 week10 #6c

Using L'Hospital's Rule to evaluate a limit representing a derivative at a point

MLC WIR 20B M151 week10 #8a

Evaluating the limit at infinity of a rational function

Review for the Common Exam: MATH 151 Exam 1 Review Problems 26-35

Review of the limit definition of a derivative and calculating the derivative

Review for the Common Exam: MATH 151 Exam 3 Review Problems 8-15

Review of limits and derivatives of inverse trigonometric functions

Limits: MATH 151 Problems 6-20

Evaluating limits of functions

Limits: MATH 151 Problems 6-20

Evaluating Limits of Functions

Continuity: MATH 151 2.5 Problems 1-6

Continuity of Functions and the Intermediate Value Theorem

Continuity: MATH 171 Problems 6 & 7

Proving a piecewise function and a polynomial are continuous

Limits and Asymptotes: MATH 151 2.6 Problems 7-11

Limits at infinity and asymptotes, along with physics applications

Limits and Asymptotes: MATH 151 2.7 Problems 7-11

Limits at infinity, asymptotes, and tangent lines

Derivatives and Rates of Change: MATH 171 Problems 1-3

Using the limit definition to find derivatives of functions and vector functions

Review for the Common Exam: MATH 151 3.1 Exam 1 Review Problems 26-35

Review of the limit definition of a derivative and calculating the derivative

Review for the Common Exam: MATH 151 3.2 Exam 1 Review Problems 26-35

Review of the limit definition of a derivative and calculating the derivative

Riemann Sums and Definite Integrals: MATH 151 5.2 Problems 6-12

Using Reimann sums and the Fundamental Theorem of Calculus

Riemann Sums and Definite Integrals: MATH 151 5.3 Problems 6-12

Using Riemann sums and the Fundamental Theorem of Calculus

WIR2 20B M251 V7

Finding the limit of a three-dimensional vector function

Review for the Common Exam: MATH 151 Exam 1 Review Problems 14-25

Review of limits, continuity, and the Intermediate Value Theorem

Review for the Common Exam: MATH 151 Exam 1 Review Problems 26-35

Review of the limit definition of a derivative and calculating the derivative

Review for the Common Exam: MATH 151 Exam 3 Review Problems 8-15

Review of limits and derivatives of inverse trigonometric functions

MATH 140 5.5 Exercise 1

Finding the domain of a piecewise function and evaluating it

MATH 140 5.3 Exercise 1

Finding the domain, intercepts, asymptotes, and holes of a rational function

MATH 140 5.3 Exercise 2

Finding the domain, intercepts, asymptotes, and holes of a rational function

MATH 140 5.3 Exercise 3

Finding the domain, intercepts, asymptotes, and holes of a rational function

MATH 140 5.3 Exercise 4

Adding and simplifying rational functions

MATH 140 5.3 Exercise 5

Subtracting rational functions and then simplifying the result

MATH 140 5.3 Exercise 6

Multiplying two rational functions and simplifying the result

MATH 140 5.3 Exercise 7

Dividing rational functions and simplifying the result

MATH 140 5.3 Exercise 8

Dividing and subtraction rational functions and simplifying the result

MATH 140 5.3 Exercise 9

Computing and simplifying the difference quotient for a rational function

Continuity of a Function with a Cube Root

Finding where a function with a fraction and cube root is continuous

Continuity of a Function with a Square Root and Logarithm

Determining where a function with a fraction, square root, and logarithm is continuous

Continuity of a Piecewise Function

Determining where a piecewise function is continuous algebraically

Solving for a Constant so a Piecewise Function is Continuous

Solving for a constant to make a piecewise-defined function continuous for all real numbers

Average Rate of Change from a Table

Finding the average rate of change over time periods from a table

Slope of a Secant Line

Finding the slope of a secant line to a given function

Instantaneous Rate of Change of a Function

Finding the exact value of the instantaneous rate of change

Instantaneous Rate of Change of Profit

Finding the instantaneous rate of change of profit for a given price-demand function and cost function

Slope of a Tangent Line

Finding the equation of the tangent line to a function using the limit definition

Finding the Derivative of a Polynomial Using the Limit Definition

Using the limit definition to find the derivative of a polynomial

Finding the Derivative of a Root Function Using the Limit Definition

Using the limit definition to find the derivative of a square root function

Determining Where the Derivative Exists From a Graph

Determining where the derivative of a function does not exist from a graph

Finding a Derivative with Exponential Functions and Logarithms

Finding the derivative a function with a power, exponential, and logarithm

Evaluating Derivatives From a Given Table

Finding and evaluating derivatives using values given in a table

Calculating Marginal Revenue

Finding the marginal revenue given the price-demand function for a word problem

Using the Product Rule with a Logarithm

Finding a derivative of a function with a logarithm using the Product Rule

Using the Product Rule with an Exponential

Finding the derivative of a function with a square root and exponential using the Product Rule

Using the Quotient Rule on a Rational Function

Finding the derivative of a rational function using the Quotient Rule

The Quotient Rule with an Exponential

Finding the derivative of a fraction with an exponential using the Quotient Rule

Using Both the Quotient and Product Rule

Finding a derivative using both the Product and Quotient Rule

Using the Product and Quotient Rules with a Table

Finding a derivative using the Product and Quotient Rule and values given in a table

Using the Generalized Power Rule

Finding the derivative of a function using the Generalized Power Rule

Using the Generalized Exponential Rule

Using the Generalized Exponential Rule to find the derivative of a function

Using Log Properties to Simplify Before Taking the Derivative

Using logarithm properties to simplify before using the Chain Rule to find a derivative

Using Log Properties to Simplify Before Taking the Derivative 2

Using logarithm properties to simplify before using the Generalized Logarithm Rule to find a derivative

Using the Chain Rule with a Table

Using the chain rule to find derivates with some values given in a table

Calculating the Rate of Growth With Compound Interest

Finding the rate a balance is increasing for interest compounded monthly and continuously

Using the Alternate Form of the Chain Rule

Using the alternate form of the Chain Rule to find the derivative

Using Logarithmic Differentiation to Find a Derivative

Finding the derivative of a function that requires logarithmic differentiation

Using Implicit Differentiation to Find a Derivative

Using implicit differentiation to find the derivative of a function

Using Implicit Differentiation to Find a Derivative 2

Using implicit differentiation to find the derivative of a function

Solving a Related Rates Word Problem About Liquid Filling a Sphere

Finding the rate water is flowing into an expandable sphere given the rate a sphere is growing

Solving a Related Rates Word Problem About Profit

Finding the rate of change of profit given the rate of increase for sales

Solving a Related Rates Word Problem About a Sliding Ladder

Finding how fast a ladder moves up a wall as the bottom is being pushed

Finding Critical Values

Finding the critical values for several functions

Increasing and Decreasing and Local Extrema

Finding the intervals where a function is increasing/decreasing and the local extrema

Increasing and Decreasing and Local Extrema for a Revenue Function

Finding intervals of increase/decrease and the local extema for revenue from a word problem

Inflection Points and Intervals of Concavity for an Exponential Function

Finding the intervals of concavity and inflection points for a function with exponentials

Inflection Points and Intervals of Concavity from a Graph

Determining the intervals of concavity and inflection points from the graph of a function

Absolute Extrema on a Closed Interval 2

Finding the absolute maximum and absolute minimum of a rational function on two closed intervals

Local and Absolute Extrema from a Graph

Finding all local and absolute extrema of a function from a graph

Maximizing a Product of Numbers

Finding the maximum product of two numbers given their sum is 100

Finding the Price to Maximize Profit

Finding the selling price of trucks to maximize profit given the cost and price-demand functions

Finding the Box with the Largest Volume

Finding the dimensions of the box with the largest volume given the amount of material to make the box

Minimizing the Cost of a Box

Finding the minimum cost of a box given the volume and cost of materials

Finding an Antiderivative

Finding the antiderivative of a function

Finding an Indefinite Integral

Evaluating an indefinite integral with an exponential

Finding an Indefinite Integral with a Fraction

Solving an indefinite integral by first simplifying the fraction

Finding a Function from its Derivative and One Value

Solving for a function given its derivate and one value

Finding the Cost Function from Marginal Cost

Solving the antiderivative of marginal cost to find the cost function and evaluating a particular cost

u-Substitution With an Exponential Function

Solving an indefinite integral with an exponential function suing u-substitution

u-Substitution With a Natural Logarithm

Solving an indefinite integral with a natural logarithm using u-substitution

u-Substitution With a Quotient and Exponentials

Solving an indefinite integral with exponentials in a quotient using u-substitution

u-Substitution With a Quotient and a Root

Solving an indefinite integral with a cube root in the denominator using u-substitution

Finding the Function from Its Derivative Using u-Substitution

Using u-substitution in an indefinite integral to find a function from its derivative and a given vaue

Calculating Profit From Marginal Profit Using u-Substitution

Calculating profit from marginal profit using an indefinite integral and u-substitution

Calculating the Exact Area Under a Curve With Geometry

Using geometric formulas for circles, triangles, and rectangles to find the exact area under a curve

Introduction to Riemann Sums

Estimating the area under a function using right-hand, left-hand, and midpoint Riemann sums

Estimating Area With a Right-Hand Riemann Sum

Estimating the area under a curve using right-hand Riemann sums

Estimating Area With a Left-Hand Riemann Sum

Estimating the area under a curve using left-hand Riemann sums

Estimating Area With a Midpoint Riemann Sum

Estimating the area under a curve using midpoint Riemann sums

Estimating the Area Under a Curve With a Riemann Sum

Estimating the area under a graph using right-hand Riemann sums

Calculating a Definite Integral From a Graph

Calculating a definite integral by finding the area under a curve using geometry

Definite Integral Comparison Properties

Comparing two definite integrals with the same limits of integration

Evaluating a Definite Integral

Using the Fundamental Theorem of Calculus to evaluate a definite integral

Evaluating a Definite Integral 2

Using the Fundamental Theorem of Calculus to evaluate a definite integral

Evaluating a Definite Integral with u-Substitution

Using the Fundamental Theorem of Calculus and \(u\)-substitution to evaluate a definite integral

Part 1 of the Fundamental Theorem of Calculus

Using Part 1 of the Fundamental Theorem of Calculus to find the derivative of a function defined using an integral

Solving a Word Problem With a Definite Integral

Solving a word problem using a definite integral and the Fundamental Theorem of Calculus

Average Value of a Function

Finding the average value of a a function on an interval using a definite integral

Area Between Two Curves

Finding the area between two curves on an interval using a definite integral

Area of the Region Bounded by Two Curves

Finding the area of a region bounded by two curves using definite integrals

Derivatives of Exponential Functions

Explaining the formulas for the derivatives of exponential functions

Sequences

An introduction to sequences and their limits along with the limit of recurrence equations

Sequences Example 1

Finding the first few terms and limit of a sequence

Sequences Example 2

Finding the terms and limit of a recursive sequence

Trigonometric Limits Example 1

Solving a limit example with a trigonometric functions

Trigonometric Limits Example 2

Solving a limit example with a trigonometric function

Trigonometric Limits Example 3

Evaluating a trigonometric limit using trigonometric identities

Sandwich Theorem (or Squeeze Theorem)

Explaining the Sandwich (or Squeeze) Theorem with a graphical example

Sandwich Theorem Example

Solving a limit at infinity using the Sandwich (or Squeeze) Theorem

WIR7 20B M150 V13

Calculating the difference quotient for a rational function

WIR8 20B M150 V15

Calculating the difference quotient for a rational function

WIR1 20B M150 V16

Dividing rational expressions and simplifying

WIR1 20B M150 V17

Subtracting rational expressions and simplifying

WIR1 20B M150 V18

Performing operations with rational expressions and simplifying

WIR8 20B M150 V04

Performing operations with rational expressions and simplifying

WIR8 20B M150 V03

Finding the domains of expressions

WIR3 20B M150 V13

Determining the properties of a rational function and graphing it

WIR8 20B M150 V09

Determining the properties of a rational function and graphing it

Review for the Common Exam: MATH 151 Exam 2 Review Problems 1-9

Reviewing the chain rule and the derivatives and limits of trigonometric functions

Review for the Common Exam: MATH 151 Exam 2 Review Problems 21-29

Related rates problems, differentials, linear and quadratic approximations

Review for Common Exam: MATH 151 Exam 3 Review Problems 15-19

Mean Value Theorem and using derivatives to find the shape of curves

Inverse Trigonometric Functions: MATH 151 1.5 Problems 9-12

Properties and derivatives of inverse trigonometric functions

Approximations and Exponentials: MATH 151 2.6 Problems 7-14

Approximation and Newton's Method, and limits and derivatives of exponential functions

Differentials and Approximations: MATH 151 3.10 Problems 1-6

Differentials, linear approximations and quadratic approximations

Trigonometry Derivatives and the Chain Rule: MATH 151 3.3 Problems 1-9

Derivatives of trigonometric functions and using the Chain Rule

Approximations and Exponentials: MATH 151 3.4 Problems 7-14

Approximation and Newton's Method, and limits and derivatives of exponential functions

Trigonometry Derivatives and the Chain Rule: MATH 151 3.4 Problems 1-9

Derivatives of trigonometric functions and using the Chain Rule

Inverse Trigonometric Functions: MATH 151 Problems 9-12

Properties and derivatives of inverse trigonometric functions

Differentiation and Applications: MATH 151 Problems 1-8

Derivatives of exponential and logarithmic functions and the exponential model

Differentiation and Applications: MATH 151 3.8 Problems 1-8

Derivatives of exponential and logarithmic functions and the exponential model

Studying the Shape of Curves: MATH 151 4.1 Problems 2-7

Using derivatives to find properties of graphs

Mean Value Theorem and Studying the Shape of Curves: MATH 151 4.2 Problems 1-6

Mean Value Theorem and properties of a graph

Mean Value Theorem and Studying the Shape of Curves: MATH 151 4.3 Problems 1-6

Mean Value Theorem and properties of a graph

Studying the Shape of Curves: MATH 151 Problems 2-7

Using derivatives to find properties of graphs

Integration by Substitution: MATH 151 5.5 Problems 13 & 14

Examples of integration by substitution

MLC WIR 20B M151 week2 #06

Evaluating limits where the denominator approaches zero

MLC WIR 20B M151 week2 #08

Evaluating left and right limits of a fraction containing an absolute value

MLC WIR 20B M151 week2 #09

Evaluating one-sided and two-sided limits of a piecewise

MLC WIR 20B M151 week2 #10

Explaining why a piecewise function is discontinuous at a point

MLC WIR 20B M151 week2 #11

Solving for the values for constants to make a piecewise function is continuous

MLC WIR 20B M151 week3 #15

Using the Squeeze Theorem to evaluate the limit of a function

MLC WIR 20B M151 week3 #18

Solving for the value of a constant that makes a function is continuous everywhere

MLC WIR 20B M151 week4 #1h

Using the Quotient Rule to differentiate a rational function

MLC WIR 20B M151 week7 #4b

Evaluating a limit using L'Hospital's Rule

MLC WIR 20B M151 week7 #4c

Evaluating a limit using L'Hospital's Rule

MLC WIR 20B M151 week7 #4d

Evaluating a limit using L'Hospital's Rule

MLC WIR 20B M151 week7 #4e

Evaluating a limit with an indeterminate product using L'Hospital's Rule

MLC WIR 20B M151 week7 #4f

Evaluating a limit with an indeterminant difference using L'Hospital's Rule

MLC WIR 20B M151 week7 #4g

Evaluating a limit with an indeterminate power using L'Hospital's Rule

MLC WIR 20B M151 week7 #4h

Evaluating a limit with an indeterminant power using L'Hospital's Rule

MLC WIR 20B M151 week7 #3

Sketching a curve given information about the function and its derivatives

MLC WIR 20B M151 week9 #8c

Evaluating a limit using L'Hospital's Rule

MLC WIR 20B M151 week9 #8d

Evaluating a limit with an indeterminant power using L'Hospital's Rule

MLC WIR 20B M151 week9 #8e

Evaluating a limit with an indeterminant product using L'Hospital's Rule

MLC WIR 20B M151 week9 #8f

Evaluating a limit with an indeterminant product using L'Hospital's Rule

MLC WIR 20B M151 week9 #10b

Finding the antiderivative of a rational function

MLC WIR 20B M151 week9 #13

Using a limit of Riemann sums to write an expression for the area under a graph

MLC WIR 20B M151 week10 #8b

Evaluating the limit of a function at negative infinity

MLC WIR 20B M151 week10 #8c

Evaluating the limit at infinity of a fraction with exponential functions

MLC WIR 20B M151 week10 #8d

Evaluating the limit at negative infinity of a fraction with exponential functions

MLC WIR 20B M151 week10 #8e

Evaluating a limit at infinity by combining logarithms

MLC WIR 20B M151 week10 #19a

Using L'Hospital's Rule to solve a limit

MLC WIR 20B M151 week10 #19b

Using L'Hospital's Rule to solve a limit with an indeterminant product

MLC WIR 20B M151 week10 #19c

Using L'Hospital's Rule to solve a limit with an indeterminant difference

MLC WIR 20B M151 week10 #19d

Using L'Hospital's Rule to solve a limit with an indeterminant power

MLC WIR 20B M151 week10 #24b

Evaluating a definite integral by first simplifying the integrand

MLC WIR 20B M151 week10 #7

Solving for a constant so that a piecewise function is continuous

Review for the Common Exam: MATH 152 Exam 1 a Review Problems 1-4

Reviewing u-Substitution

Review for the Common Exam: MATH 152 Exam 1 b Review Problem 36

Review of partial fractions

Review for the Common Exam: MATH 152 Exam 3 b Review Problems 1-3

Review of sequences and finding the sum of a series

Review for the Common Exam: MATH 152 Exam 1 b Review Problems 34 & 35

Review of partial fractions

WIR 20B M152 V68

Determining if a series is absolutely convergent, conditionally convergent, or divergent. 

WIR 20B M152 V69

Determining if a series is absolutely convergent, conditionally convergent, or divergent. 

WIR 20B M152 V70

Determining if a series is absolutely convergent, conditionally convergent, or divergent. 

WIR 20B M152 V71

Determining if a series is absolutely convergent, conditionally convergent, or divergent. 

WIR 20B M152 V72

Determining if a series is absolutely convergent, conditionally convergent, or divergent. 

WIR 20B M152 V75

Finding the interval and radius of convergence for a power series

WIR 20B M152 V2

Integrating a rational function using u-substitution

WIR 20B M152 V3

Integrating a rational function using u-substitution

MATH 152: u-Substitution Exercise 3

Using u-substitution to integrate a rational function

Cases for Partial Fraction Decomposition

Explaining all four cases of partial fraction decomposition

MATH 152: Partial Fraction Decomposition Exercise 1

Using partial fraction decomposition to rewrite and then integrate a rational function

MATH 152: Partial Fraction Decomposition Exercise 2

Using partial fraction decomposition to rewrite and then integrate a rational function

MATH 152: Partial Fraction Decomposition Exercise 3

Using partial fraction decomposition to rewrite and then integrate a rational function

MATH 152: Partial Fraction Decomposition Exercise 5

Using partial fraction decomposition to rewrite and then integrate a rational function

MATH 152: Partial Fraction Decomposition Exercise 6

Using partial fraction decomposition to rewrite and then integrate a rational function

WIR 20B M152 V36

Determining if an improper integral converges or diverges

WIR 20B M152 V37

Determining if an improper integral converges or diverges

WIR 20B M152 V38

Determining if an improper integral converges or diverges

WIR 20B M152 V39

Determining if an improper integral converges or diverges

Vector Functions: MATH 171 Problems 1 & 2

Proving a certain parameterization gives the unit circle and showing vector equations of lines are parallel

Vectors and Derivatives (Product Rule): MATH 171 Problems 1-3

Proving facts about the derivatives of vector functions including the product rule

Derivatives and Applications: MATH 171 Problems 7 & 8

Calculating slopes of tangent lines to parametric curves

Review for the Common Exam: MATH 151 Exam 2 Review Problems 1-9

Reviewing the chain rule and the derivatives and limits of trigonometric functions

Review for the Common Exam: MATH 151 Exam 2 Review Problems 21-29

Related rates problems, differentials, linear and quadratic approximations

Review for Common Exam: MATH 151 Exam 3 Review Problems 15-19

Mean Value Theorem and using derivatives to find the shape of curves

Inverse Trigonometric Functions: MATH 151 1.5 Problems 9-12

Properties and derivatives of inverse trigonometric functions

Limits: MATH 171 Problem 7

Proving a property for limits of sums using the epsilon-delta definition

Limits: MATH 171 Problems 8 & 9

Proving a property of scalar multiplication for limits using the epsilon-delta definition and using the Squeeze Theorem for Limits.

Precise Definition of a Limit: MATH 171 Problems 3 & 4

Proving limits using the epsilon-delta definition

Precise Definition of a Limit: MATH 171 Problems 5 & 6

Proving limits using the epsilon-delta definition

Continuity: MATH 171 Problems 8 & 9

Proving a product of continuous functions is continuous and using the Intermediate Value Theorem

Limits and Asymptotes: MATH 171 Problem 5

Proving a property for the limit of the difference of functions as x approaches infinity

Limits and Asymptotes: MATH 171 Problems 1 & 2

Proving the values of limits as x approaches infinity using the epsilon-delta definition

Limits and Asymptotes: MATH 171 Problems 3 & 4

Proving the values of limits as x approaches infinity using the epsilon-delta definition

Approximations and Exponentials: MATH 151 2.6 Problems 7-14

Approximation and Newton's Method, and limits and derivatives of exponential functions

Differentiation Formulas: MATH 171 Problems 6 & 7

Proving the Product Rule and the rule for the derivative of a difference of functions

Differentials and Approximations: MATH 151 3.10 Problems 1-6

Differentials, linear approximations and quadratic approximations

Higher Order Derivatives: MATH 171 Problems 4-6

Finding a formula for a higher order derivative and a formula for the second derivative of a product

Trigonometry Derivatives and the Chain Rule: MATH 171 Problems 1-3

Proving the derivatives of trigonometric functions and that sine is continuous

Trigonometry Derivatives and the Chain Rule: MATH 151 3.3 Problems 1-9

Derivatives of trigonometric functions and using the Chain Rule

Approximations and Exponentials: MATH 151 3.4 Problems 7-14

Approximation and Newton's Method, and limits and derivatives of exponential functions

Trigonometry Derivatives and the Chain Rule: MATH 151 3.4 Problems 1-9

Derivatives of trigonometric functions and using the Chain Rule

Inverse Trigonometric Functions: MATH 151 Problems 9-12

Properties and derivatives of inverse trigonometric functions

Differentiation and Applications: MATH 151 Problems 1-8

Derivatives of exponential and logarithmic functions and the exponential model

Derivatives of Logarithmic Functions: MATH 171 Problems 7-9

Proving facts about logarithms and exponentials including the derivative of an exponential with an arbitrary base

Absolute Extrema: MATH 171 Problems 4 & 5

Proving Fermat's Theorem and graphing local and absolute extrema

Studying the Shape of Curves: MATH 151 4.1 Problems 2-7

Using derivatives to find properties of graphs

Mean Value Theorem and Studying the Shape of Curves: MATH 151 4.2 Problems 1-6

Mean Value Theorem and properties of a graph

Mean Value Theorem and Studying the Shape of Curves: MATH 151 4.3 Problems 1-6

Mean Value Theorem and properties of a graph

Studying the Shape of Curves: MATH 151 Problems 2-7

Using derivatives to find properties of graphs

L'Hospital's Rule: MATH 171 Problems 7-9

Proving L'Hospital's Rule and using it to evaluate limits

Definite Integrals: MATH 171 Problems 5-9

The definition and properties of definite integrals

Fundamental Theorem of Calculus: MATH 171 Problems 1-3

Proving and then applying the Fundamental Theorem of Calculus

Integration by Substitution: MATH 151 5.5 Problems 13 & 14

Examples of integration by substitution

Review for the Common Exam: MATH 152 Exam 1 a Review Problems 1-4

Reviewing u-Substitution

Review for the Common Exam: MATH 152 Exam 1 b Review Problem 36

Review of partial fractions

Review for the Common Exam: MATH 152 Exam 3 b Review Problems 1-3

Review of sequences and finding the sum of a series

Review for the Common Exam: MATH 152 Exam 1 b Review Problems 34 & 35

Review of partial fractions

Limit of a Sequence: MATH 172 Problems 1-5

Using the precise definition for the limit of a sequence and proving the Squeeze Theorem

Monotone Sequence Theorem: MATH 172 Problems 6-8

Using the Monotone Sequence Theorem and induction to show a sequence converges

Taylor and Maclaurin Series: MATH 172 Problems 1-5

Reviewing Taylor and Maclaurin Series and Taylor's Inequality

Infinite Series: MATH 172 Problems 1-3

The definition of convergent series and the Divergence Test

The Sum of a Series

Defining the sum of a series as the limit of the sequence of partial sums

Test for Divergence

Explaining how to use the Test for Divergence for an infinite series

Finding the Sum of a Series

Finding the sum of a series when you know the sequence of partial sums

Alternating Series and Ratio Tests: MATH 172 Problems 8-10

Proving the Alternating Series and Ratio Test and covers absolute convergence

Power Series: MATH 172 Problems 1-3

Covering Radius and Interval of Convergence of Power Series

Integration Using Partial Fractions: MATH 172 Problems 8 & 9

Finding a partial fraction decomposition and integrating using partial fractions

Cases for Partial Fraction Decomposition

Explaining all four cases of partial fraction decomposition

Improper Integrals: MATH 172 Problems 3-5

Definition of Improper Integrals and using the Comparison Theorem to determine convergence or divergence

Hydrostatic Force: MATH 172 Problems 6 & 7

Using Riemann Sums and Integrals to calculate hydrostatic force

WIR2 20B M251 V6

Determining the domain of a three-dimensional vector function

WIR 20B M152 V45

Determining if a sequence converges or diverges

WIR 20B M152 V46

Determining if a sequence converges or diverges

WIR 20B M152 V47

Determining if a sequence converges or diverges

WIR 20B M152 V48

Determining if a sequence is increasing, decreasing, or not monotonic and if it is bounded

WIR 20B M152 V49

Determining if a sequence is increasing, decreasing, or not monotonic and if it is bounded

WIR 20B M152 V50

Determining the limit of a bounded and increasing sequence

MATH 152: Sequences Exercise 4

Finding the limit of a sequence

MATH 152: Sequences Exercise 5

Finding the limit of a sequence with an arcsin

MATH 152: Sequences Exercise 6

Finding the limit of a sequence using logarithm properties

MATH 152: Sequences Exercise 7

Finding the limit of a sequence

Multivariable Limits Conceptual V1

Explaining how to calculate the limit of a surface for two dimensional functions

Multivariable Limits Conceptual V2

Explaining the definition of the limit of a function of two variables

Multivariable Limits Conceptual V3

Explaining limits of functions of two variables that approach infinity

Multivariable Limits Exercise 1

Solving several limits of functions of two variables

Multivariable Limits Exercise 2

Finding the limit of a function of two variables

Multivariable Limits Exercise 3

Solving a limit of a function of two variables

Multivariable Limits Exercise 4

Solving a limit of a function of two variables

Cases for Partial Fraction Decomposition

Explaining all four cases of partial fraction decomposition

Multivariable Limits Conceptual V1

Explaining how to calculate the limit of a surface for two dimensional functions

Multivariable Limits Conceptual V2

Explaining the definition of the limit of a function of two variables

Multivariable Limits Conceptual V3

Explaining limits of functions of two variables that approach infinity

WIR2 20B M150 V7

Solving a rational equation and checking the solutions

Math 140 Exam 3 Review Exercise 5

Finding the domain, intercepts, holes, and vertical asymptotes for a rational function

Math 140 Exam 3 Review Exercise 7

Compute and simplify the difference quotient for a rational function

Simplifying a Rational Expression

Simplifying a rational expression

Subtracting Rational Expressions

Adding and then simplifying two rational expressions

Multiplying Rational Expressions

Multiplying two rational expressions and then simplifying

Dividing Rational Expressions

Dividing rational expressions and then simplifying the answer

Adding Rational Expressions

Adding two rational expressions and then simplifying the answer

Holes and Asymptotes of Rational Functions

Finding any holes, vertical asymptotes, and horizontal asymptotes of a rational function

Holes and Asymptotes of Rational Functions (2)

Finding any holes, vertical asymptotes, and horizontal asymptotes of a rational function

Matching a Rational Function with its Graph

Matching a rational function with its graph

Domain of a Rational Function

Finding the domain of a rational function

Domain of a Rational Function (2)

Finding the domain of a rational function

Function Composition with a Rational Function

Finding the composition of a rational function and a quadratic

Inverse of a Rational Function

Finding the inverse of a rational function and its domain

Inverse of a Rational Function (2)

Finding the inverse of a rational function and its domain

Difference Quotient of a Rational Function

Finding and simplifying the difference quotient for a rational function

Difference Quotient of a Square Root Function

Finding and simplifying the difference quotient for a square root function

Solving an Inequality with a Rational Function

Solving an inequality with a rational expression by factoring and using a sign diagram

Solving an Inequality with a Sum of Rational Functions

Solving an inequality with two rational expressions using a sign diagram

Solving an Inequality with by Finding a Least Common Denominator

Solving an inequality with a rational expression using a sign diagram

A Composition of Tangent and Arccosine

Evaluating a composition of tangent and arccosine

Convergence in Probability

Defining convergence for random variables in probability

Convergence in Probability Exercise 1

Proving that a sequence of random variables converges in probability

The Sum of a Series

Defining the sum of a series as the limit of the sequence of partial sums

Test for Divergence

Explaining how to use the Test for Divergence for an infinite series

Finding the Sum of a Series

Finding the sum of a series when you know the sequence of partial sums

Math 152: Series Exercise 2

Finding the first four terms of several given series

Math 152: Series Exercise 3

Determining if a series diverges by the Test for Divergence

Math 152: Series Exercise 5

Finding the sum of a series given a formula for the partial sums

WIR 20B M152 V51

Determining if a series converges or diverges

WIR 20B M152 V59

Using the limit comparison test to determine if a series converges or diverges

WIR 20B M152 V60

Using the limit comparison test to determine if a series converges or diverges

WIR 20B M152 V61

Using the limit comparison test to determine if a series converges or diverges

Math 152: Comparison Tests Exercise 8

Using the Limit Comparison Test to determine if a series converges or diverges

Math 152: Comparison Tests Exercise 9

Using the Limit Comparison Test to determine if a series converges or diverges

Math 152: Comparison Tests Exercise 10

Using the Limit Comparison Test to determine if a series converges or diverges

WIR 20B M152 V62

Using the Alternating Series Test to determine if a series converges or diverges

WIR 20B M152 V63

Using the Alternating Series Test to determine if a series converges or diverges

WIR 20B M152 V64

Using the Alternating Series Test to determine if a series converges or diverges

WIR 20B M152 V65

Determining if an Alternating Series converges or diverges

Creating and Manipulating Symbolic Expressions in Python

Creating symbolic expression in Python and then factoring, expanding, and simplifying the expressions

List Comprehension and Numerical, Graphical, and Symbolic Limits in Python

Using Python to numerically estimate a limit, graphically estimate a limit, and find the exact limit

Simplifying Difference Quotients in Python

Using Python to simplify a difference quotient and find a derivative using the limit definition

Generating and Plotting Partials Sums of a Series in Python

Using Python to calculate the partial sums of a series to estimate the value of the series

Generating and Plotting Sequences in Python

Using Python to numerically, graphically, and analytically find the limit of a sequence

Domain of Rational Functions Video 1

Finding the domain of several rational functions

Domain of Rational Functions Video 2

Finding the domain of a rational function

Domain of Rational Functions Video 3

Explaining how to find any holes and vertical asymptotes of a rational function

Domain of Rational Functions Video 4

Finding the domain of a rational function using factoring

Domain of Combinations of Functions Video 1

Finding the domain of a function with a denominator, square root, and logarithm

Properties of Rational Functions and Expressions Video 4

Finding horizontal asymptotes for rational functions

Properties of Rational Functions and Expressions Video 5

Determining the end behavior and horizontal asymptotes for rational functions

Properties of Rational Functions and Expressions Video 1

Discussing parent functions of rational functions and their properties

Properties of Rational Functions and Expressions Video 2

Finding horizontal asymptotes for rational functions

Properties of Rational Functions and Expressions Video 3

Explaining how to do polynomial long division

Properties of Rational Functions and Expressions Video 7

How to simplify rational expressions

Properties of Rational Functions and Expressions Video 8

Adding and subtracting rational expressions by finding a common denominator

Properties of Rational Functions and Expressions Video 9

Explaining how to multiply and divide rational expressions

Properties of Rational Functions and Expressions Video 10

Performing algebraic operations with rational expressions and simplifying the answer

Solving Rational Equations Video 1

Solving equations that contain rational expressions

Solving Rational Equations Video 2

Solving an equation that contains rational expressions

Solving Rational Equations Video 3

Solving an equation that contains rational expressions

Derivatives of Exponential Functions

Explaining the formulas for the derivatives of exponential functions

Introduction to Riemann Sums

Estimating the area under a function using right-hand, left-hand, and midpoint Riemann sums