Properties of Radical Functions and Expressions Video 2
How to rewrite radical terms as power terms
How to rewrite radical terms as power terms
Simplifying an expression with both power and exponential functions using properties of exponents
Explaining how to solve equations with power and exponential terms
Properties of exponents applied to power and exponential expressions
Properties of exponents applied to power and exponential expressions
Simplifying power and exponential expressions using properties of exponents
Simplifying power and exponential expressions using properties of exponents
Simplifying power and exponential expressions using properties of exponents
Properties of exponential growth and decay functions
Properties of the exponential function with base e
Solving equations with exponential terms
Solving equations with base e exponential terms
Solving an equation with exponential functions
Solving an equation with exponential functions
Writing a non-linear function to represent the line graphed on a semilog plot
Using the second derivative to find the maximum rate of change in a word problem
Determining divergence or convergence of improper integrals
Determining divergence or convergence of improper integrals
Finding the domain of a function with a root and a logarithm in the denominator
Explaining how to solve radical equations and then solving example problems
Solving equations with odd radicals
Explaining the terminology and rules of logarithms
Explaining how to solve logarithmic equations
Solving logarithmic equations with a single logarithm term
Solving logarithmic equations with multiple logarithm terms
Solving logarithmic equations with multiple logarithm terms on both sides
Finding the properties of an exponential function including domain, range, end behavior, and intercepts
Finding the properties of an exponential function including domain, range, end behavior, and intercepts
Finding the properties of an exponential function including domain, range, end behavior, and intercepts
Finding the domain of a function that is a fraction containing an exponential and root
Finding the domain of a function that is a fraction containing an exponential and root
Finding the domain of a function that is a fraction containing exponentials and a square root
Calculating how much to invest with continuously compounded interest
Identifying the parent function and transformations for a given graph
Examples of calculating infinite limits with exponentials in a rational function
Examples of finding derivatives and calculating approximate profit
Using integrals to solve application problems
Limits with exponential functions
Determining where functions are continuous
Using the power rule to find derivatives
Examples of differentiating exponential and logarithmic functions
More examples using u-Substitution
Solving more application problems using definite integrals
Application problems finding the average value of a function
Solving examples finding the area between curves
The definition of higher derivatives and solving an example
Using derivatives to find the velocity and acceleration functions from the position function
Explaining the formulas for the derivatives of exponential functions
Calculating the derivative of a function with exponentials using the chain and product rule
Calculating a derivative of a quotient with an exponential function
Explaining exponential functions in discrete time
Solving a population example of exponential growth in discrete time
Solving a population grown example on recurrence equations
Explaining the definition of logarithmic scale and double-log plots
Explaining the logarithmic scale and a semilog plot
Using logarithms to transform a power function into a linear function
Writing a non-linear function for the graph containing two points on a double-log plot
Using logarithms to transform an exponential function to a linear function
Simplifying a fraction using properties of exponents
Simplifying a fraction containing fractional exponents
Simplifying a fraction with negative exponents
Determining properties of an exponential function
Determining properties of an exponential function
Determining properties of an exponential function
Identifying the graph of an exponential function
Solving an equation with an exponential function
Determining properties of an exponential function
Solving an equation with an exponential function
Solving an equation with an exponential function
Solving an equation with an exponential function
Solving an equation with exponential functions by factoring
Solving an equation with logarithmic functions
Solving an equation with logarithmic functions
Solving an equation with logarithmic functions
Solving an equation with logarithmic functions
Solving an equation with logarithmic functions
Modeling a population size with an exponential function
Review of limits and derivatives of inverse trigonometric functions
Derivatives of exponential functions and the exponential model
Review of limits and derivatives of inverse trigonometric functions
Mean Value Theorem and using derivatives to find the shape of curves
Antiderivatives and physics applications
Approximation and Newton's Method, and limits and derivatives of exponential functions
Approximation and Newton's Method, and limits and derivatives of exponential functions
Derivatives of exponential and logarithmic functions and the exponential model
Derivatives of exponential and logarithmic functions and the exponential model
Mean Value Theorem and properties of a graph
Mean Value Theorem and properties of a graph
Using L'Hospital's Rule to solve limits
Using Reimann sums and the Fundamental Theorem of Calculus
Using Reimann sums and the Fundamental Theorem of Calculus
Examples of integration by substitution
Differentiating a function with an exponential function and using the Power Rule
Using the Product Rule to differentiate a function
Using the Quotient Rule to differentiate a function
Using the Product and Quotient Rules to differentiate a function
Using the Product Rule to find a first and second derivative
Using the Chain Rule to differentiate functions with exponential and trigonometric functions
Using the Chain Rule to find a first and second derivative
Using the Chain Rule to find the pattern for a higher order derivative
Finding the derivative using implicit differentiation
Using logarithmic differentiation to find the derivative of a function
Using logarithmic differentiation to find the derivative of a function
Using logarithmic differentiation to find the derivative of a function
Using the Product and Chain Rule to find several derivatives
Using the Product, Quotient and Chain Rules to find several derivatives
Using the Quotient and Chain Rules to find several derivatives
Using the Product and Chain Rules to differentiate functions with logarithms
Differentiating functions with logarithmic and inverse trigonometric functions
Differentiating functions with inverse trigonometric functions
Finding the derivative of an implicit function
Finding the derivative of an implicit function
Evaluating a limit using L'Hospital's Rule
Evaluating a limit with an indeterminate product using L'Hospital's Rule
Evaluating a limit with an indeterminant difference using L'Hospital's Rule
Evaluating a limit with an indeterminate power using L'Hospital's Rule
Evaluating a limit with an indeterminant power using L'Hospital's Rule
Antidifferentiating twice to find a function from its second derivative
Antidifferentiating twice to find a function from its second derivative
Antidifferentiating to find a function from its derivative
Antidifferentiating twice to find a function from its second derivative
Antidifferentiating twice to find a function from its second derivative
Using antidifferentiation to find the height of a cliff from the impact speed of a dropped stone
Evaluating a limit using L'Hospital's Rule
Evaluating a limit with an indeterminant power using L'Hospital's Rule
Evaluating a limit with an indeterminant product using L'Hospital's Rule
Finding the antiderivative of a function and using a function value to find the constant
Evaluating the limit at infinity of a fraction with exponential functions
Evaluating the limit at negative infinity of a fraction with exponential functions
Finding a derivative using the Chain Rule and Product Rule
Using L'Hospital's Rule to solve a limit with an indeterminant power
Evaluating a definite integral with an exponential and sine function
Examples reviewing integration techniques from Calculus I
Review of improper integrals and the Comparison Theorem
Review of Taylor and Maclaurin Series and their properties
Review of Taylor Polynomials and Taylor's Inequality
Finding Taylor and Maclaurin Series for functions
Examples of integration by substitution
Using the disk, washer, and shell method to find a volume of revolution
Finding volume using using disks, washers and the shell method
Examples using integration by parts
Integrating an exponential function using u-substitution
Finding the area of a region bounded by curves
Evaluating an integral using integration by parts
Evaluating an integral using integration by parts
Using the comparison test to determine if an improper integral converges or diverges
Determining if a series converges or diverges and find the sum if it converges
Using the comparison test to determine if a series converges or diverges
Using the limit comparison test to determine if a series converges or diverges
Determining if a series is absolutely convergent, conditionally convergent, or divergent.
Finding the Taylor polynomial of a function
Finding the length of a curve given by parametric equations
Finding the area of a region defined using polar coordinates
Solving an indefinite integral with an exponential function using integration by parts
Solving a definite integral with an exponential function using integration by parts
Solving an indefinite integral with an exponential function using integration by parts
Using integration by parts twice for an integral with sine and an exponential function
Using u-substitution on an indefinite integral with an exponential function, sine, and cosine
Using u-substitution to solve an indefinite integral with an exponential function
Review of limits and derivatives of inverse trigonometric functions
Derivatives of exponential functions and the exponential model
Review of limits and derivatives of inverse trigonometric functions
Mean Value Theorem and using derivatives to find the shape of curves
Antiderivatives and physics applications
Approximation and Newton's Method, and limits and derivatives of exponential functions
Using the limit definition to find a derivative and proving the power rule
Using the limit definition to find a derivative and proving the power rule
Examples involving the tangent line to an exponential function and finding the derivative of hyperbolic cosine
Approximation and Newton's Method, and limits and derivatives of exponential functions
Using implicit differentiation to solve a problem and to prove the power rule for rational exponents
Proving facts about logarithms and exponentials including the derivative of an exponential with an arbitrary base
Proving the derivative of ln(x) and the power and product rules using logarithmic differentiation
Derivatives of exponential and logarithmic functions and the exponential model
Mean Value Theorem and properties of a graph
Mean Value Theorem and properties of a graph
Using L'Hospital's Rule to solve limits
Using Reimann sums and the Fundamental Theorem of Calculus
Using Reimann sums and the Fundamental Theorem of Calculus
Examples of integration by substitution
Examples reviewing integration techniques from Calculus I
Review of improper integrals and the Comparison Theorem
Review of Taylor and Maclaurin Series and their properties
Review of Taylor Polynomials and Taylor's Inequality
Finding Taylor and Maclaurin Series for functions
Examples of integration by substitution
Using the disk, washer, and shell method to find a volume of revolution
Finding volume using using disks, washers and the shell method
Examples using integration by parts
Finding the limit of a three-dimensional vector function
Finding the partial derivatives of a function of two variables
Finding all second-order partial derivatives of a function of two variables
Evaluating a double integral over a given region
Evaluating a double integral by reversing the order of integration
Evaluating a line integral along a curve
Evaluating a line integral along a curve in space
Finding the curl and divergence of a three dimensional vector field
Evaluating a surface integral of a vector field
Using Python to approximate a definite integral using left endpoint Riemann sums
Performing basic numerical calculations in Python
Showing how the exponential function is the solution to an initial value problem
Finding the domain of a function with a denominator, square root, and logarithm
Finding the domain of a function with a natural logarithm and denominator
Finding the domain of a function with a square root in the denominator
Finding the domain of a logarithmic function
Finding the domain of even and odd roots
Finding the domain of functions with even and odd roots
Finding the domain of several rational functions
Finding the domain of a rational function
Explaining how to find any holes and vertical asymptotes of a rational function
Finding the domain of a rational function using factoring
Explaining domain restrictions for denominators, even roots, and logarithms
Explaining the main three forms for linear equations
Discussing properties of linear functions
Discussing the types of linear graphs including horizontal and vertical lines and their properties
Discussing how to write the equation of a line through two given points
Writing a linear equation of profit from a business word problem
Solving a linear equation algebraically and showing how this relates to the graph
Solving a linear equation algebraically
Solving a linear equation algebraically and showing how this relates to the graph
Explaining the format and possible solutions for a system of two linear equations
Solving a system of linear equations with two variables
Solving a system of two linear equations with two variables using the elimination method
Solving a system of two linear equations using a TI-84 calculator
Solving a system of two linear equations using a TI-84 calculator
Solving a system of two linear equations using a TI-84 calculator
Explaining the standard form for a quadratic equation and the possible number of solutions
Solving quadratic equations with the difference of two squares formula
Solving quadratic equations by factoring
Solving a quadratic equation by factoring
Solving a quadratic equation by factoring
Solving quadratic equations with the quadratic formula and discussing the number of possible solutions
Explaining when a quadratic equation does not have a real solution
Explaining the graph and properties for the parent function of quadratics
Discussing properties of quadratic functions including the vertex, domain, range, and end behavior
Solving equations with multiple radicals
Solving equations with even roots and checking the solutions
Explaining the general properties of even and odd root functions
Explaining the basic properties of logarithmic functions
Expanding logarithmic expressions using logarithm rules
Condensing a logarithmic expression into a single logarithm
Discussing parent functions of rational functions and their properties
Finding horizontal asymptotes for rational functions
Explaining how to do polynomial long division
Finding horizontal asymptotes for rational functions
Determining the end behavior and horizontal asymptotes for rational functions
Explaining basic algebraic operations for fractions
How to simplify rational expressions
Adding and subtracting rational expressions by finding a common denominator
Explaining how to multiply and divide rational expressions
Performing algebraic operations with rational expressions and simplifying the answer
Solving equations that contain rational expressions
Solving an equation that contains rational expressions
Solving an equation that contains rational expressions
Explaining the format and possible solutions for a system of two linear equations