How-To Calculus
Recommended Level: MATH 142
Limits, Derivatives, and Applications of Derivatives
The following videos explain topics you will see in Calculus I, including limits, derivatives, and applications of derivatives. These videos are helpful for any calculus course, but are particularly focused on the concepts and problems seen in MATH 142.Click the playlist you are interested in to go straight to those videos. Or you can scroll down through the page to look through all the videos yourself.
11 videos
Introduction to Limits An introduction to evaluating limits graphically, numerically, and algebraically |
6 videos
Limits: At Infinity and Infinite Solving limits at infinity and limits that may have infinite behavior |
5 videos
Continuity Determining where functions are continuous algebraically and using graphs |
6 videos
Average and Instantaneous Rate of Change Finding the average and instantaneous rate of change and the slope of secant and tangent lines |
4 videos
Limit Definition of the Derivative Using the limit definition to find the derivatives of functions and determining where the derivative exists from a graph |
18 videos
Calculating Derivatives Finding derivatives of common functions and using the product, quotient and chain rules with several business applications |
6 videos
Implicit Differentiation and Related Rates Finding derivatives with implicit differentiation and logarithmic differentiation and solving related rates problems |
8 videos
Analyzing Graphs with Derivatives Finding critical values, extrema, and inflection points; finding intervals where the function is increasing or decreasing and concave upward or downward |
7 videos
Absolute Extrema and Optimization Finding the absolute maximum and minimum on closed intervals; solving word problems by optimizing functions with given constraints |
28 videos
Antiderivatives and Integrals Finding antiderivatives of functions and solving indefinite integrals including examples using \(u\)-substitution; estimating area under curves with Riemann sums; finding the average value of a function; finding the area between curves |
These videos are an introduction to solving limits graphically, numerically, and algebraically.
These videos contain limits of fractions where the numerator and denominator both approach zero, and the limit may have infinite behavior.
Evaluating Limits from a Graph
|
Evaluating One-Sided Limits from a Graph
|
Evaluating a Limit Numerically
|
These videos contain limits of functions that are solved algebraically. The first video uses properties of limits to solve limits of combinations of functions.
Combinations of Limits from Graphs
|
Evaluating Limits Algebraically
|
Limit of a Piecewise Function
|
Limit of a Rational Function
|
Limit of a Rational Function (2)
|
Limit with Multiple Fractions
|
Limit of a Fraction with a Square Root
|
Limit with an Absolute Value
|
These videos solve limits at infinity and limits that may have infinite behavior. They also find horizontal asymptotes, vertical asymptotes, and holes of functions.
Limit at Negative Infinity of a Rational Function
|
Limits at Infinity of a Rational Function
|
Limits at Infinity of a Rational Function (2)
|
Limits at Infinity of a Fraction with Exponential Functions
|
Vertical Asymptotes and Holes of a Rational Function
|
Horizontal Asymptote of a Fraction with Exponential Functions
|
These videos determine using graphs and algebraically where functions are continuous. The examples include functions with fractions, even or odd roots, logarithms, and piecewise functions.
Where the Graph of a Function is Not Continuous
|
Continuity of a Function with a Cube Root
|
Continuity of a Function with a Square Root and Logarithm
|
Continuity of a Piecewise Function
|
Solving for a Constant so a Piecewise Function is Continuous
|
These videos find the average and instantaneous rate of change. The videos also include finding the the slope of secant lines and tangent lines of functions.
Average Rate of Change from a Table
|
Slope of a Secant Line
|
Instantaneous Rate of Change of a Function
|
Instantaneous Rate of Change of a Rational Function
|
Instantaneous Rate of Change of Profit
|
Slope of a Tangent Line
|
These videos use the limit definition to find the derivatives of functions. Also, the last video shows how to determine from a graph when the derivative exists.
Finding the Derivative of a Polynomial Using the Limit Definition
|
Finding the Derivative of a Rational Function Using the Limit Definition
|
Finding the Derivative of a Root Function Using the Limit Definition
|
Determining Where the Derivative Exists From a Graph
|
These videos calculate the derivative of common functions such as polynomials, rational functions, exponential functions, logarithms, and root functions. The videos use derivative rules such as the power rule, product rule, quotient rule, and chain rule. These derivative rules are also used to solve business word problems.
These videos find the derivative of standard functions such as polynomials, exponential functions, logarithms, and roots.
Finding a Derivative with Exponential Functions and Logarithms
|
Finding a Derivative by First Simplifying a Rational Function
|
Evaluating Derivatives From a Given Table
|
Calculating Marginal Revenue
|
These videos find derivatives using the product rule and quotient rule.
Using the Product Rule with a Logarithm
|
Using the Product Rule with an Exponential
|
Using the Quotient Rule on a Rational Function
|
The Quotient Rule with an Exponential
|
Using Both the Quotient and Product Rule
|
Using the Product and Quotient Rules with a Table
|
Finding Marginal Cost and Marginal Average Cost
|
These videos find derivatives using the chain rule.
Using the Generalized Power Rule
|
Using the Generalized Exponential Rule
|
Using Log Properties to Simplify Before Taking the Derivative
|
Using Log Properties to Simplify Before Taking the Derivative (2)
|
Using the Chain Rule with a Table
|
Calculating the Rate of Growth With Compound Interest
|
Using the Alternate Form of the Chain Rule
|
These videos find the derivative using implicit differentiation and logarithmic differentiation. The videos also use implicit differentiation to solve related rates problems.
These videos find derivatives using implicit differentiation and logarithmic differentiation. Several videos also show how sometimes you can use logarithmic properties to simplify logarithmic functions before taking the derivative.
Using Implicit Differentiation to Find a Derivative
|
Using Implicit Differentiation to Find a Derivative (2)
|
Using Logarithmic Differentiation to Find a Derivative
|
These videos use implicit differentiation to solve related rates problems.
Solving a Related Rates Word Problem About Liquid Filling a Sphere
|
Solving a Related Rates Word Problem About Profit
|
Solving a Related Rates Word Problem About a Sliding Ladder
|
These videos find the critical values of a function, the intervals where the function is increasing and decreasing, and all local extrema.
Finding Where a Function is Increasing and Decreasing
|
Finding Critical Values
|
Increasing and Decreasing and Local Extrema
|
Increasing and Decreasing and Local Extrema for a Revenue Function
|
These videos find the inflection points of a function and the intervals of concavity. The videos also cover using the Second Derivative Test to find local extrema.
Using the Quotient Rule Twice to Find the Second Derivative
|
Inflection Points and Intervals of Concavity for an Exponential Function
|
Inflection Points and Intervals of Concavity from a Graph
|
Using the Second Derivative Test to Find Local Extrema
|
These videos find the absolute maximum and absolute minimums of functions. In particular, the videos show how to find the absolute extrema on a closed interval.
Local and Absolute Extrema from a Graph
|
Absolute Extrema on a Closed Interval
|
Absolute Extrema on a Closed Interval (2)
|
These videos show how to solve word problems where you need to maximize or minimize a function with given constraints.
Maximizing a Product of Numbers
|
Finding the Price to Maximize Profit
|
Finding the Box with the Largest Volume
|
Minimizing the Cost of a Box
|
These videos find antiderivatives of functions and solve indefinite integrals.
Finding an Antiderivative
|
Finding an Indefinite Integral
|
Finding an Indefinite Integral with a Fraction
|
Finding a Function from its Derivative and One Value
|
Finding the Cost Function from Marginal Cost
|
These videos show how to solve integrals using \(u\)-substitution.
\(u\)-Substitution With an Exponential Function
|
\(u\)-Substitution With a Natural Logarithm
|
\(u\)-Substitution With a Quotient and Exponentials
|
\(u\)-Substitution With a Quotient and Root
|
Finding the Function from Its Derivative Using \(u\)-Substitution
|
Calculating Profit From Marginal Profit Using \(u\)-Substitution
|
These videos show how to calculate the area under curves with geometry and estimate the area with Riemann sums. The videos also give properties of definite integrals.
Calculating the Exact Area Under a Curve With Geometry
|
Introduction to Riemann Sums
|
Estimating Area With a Right-Hand Riemann Sum
|
Estimating Area With a Left-Hand Riemann Sum
|
Estimating Area With Midpoint Riemann Sums
|
Estimating the Area Under a Curve With a Riemann Sum
|
Calculating a Definite Integral From a Graph
|
Properties of Definite Integrals
|
Definite Integral Comparison Properties
|
These videos show how to evaluate definite integrals using the Fundamental Theorem of Calculus and antiderivatives.
Evaluating a Definite Integral
|
Evaluating a Definite Integral (2)
|
Evaluating a Definite Integral With \(u\)-substitution
|
Part 1 of the Fundamental Theorem of Calculus
|
Solving a Word Problem With a Definite Integral
|
These videos show how to use definite integrals to find the area between two curves using definite integrals and the average value of a function on an interval.
Area Between Two Curves on an Interval
|
Area of the Region Bounded by Two Curves
|
Average Value of a Function on an Interval
|