Domain of Rational Functions Video 4
Finding the domain of a rational function using factoring
Problem: Reduce the following rational expressions, if possible.
Finding the domain of a rational function using factoring
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
Subtracting rational functions and then simplifying the result
Multiplying two rational functions and simplifying the result
Dividing rational functions and simplifying the result
Dividing and subtraction rational functions and simplifying the result
Dividing rational expressions and simplifying
Subtracting rational expressions and simplifying
Performing operations with rational expressions and simplifying
Performing operations with rational expressions and simplifying
Solving a rational equation and checking the solutions
Determining divergence or convergence of improper integrals
Determining divergence or convergence of improper integrals
Finding the limit of a three-dimensional vector function
Creating symbolic expression in Python and then factoring, expanding, and simplifying the expressions
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 several rational functions
Finding the domain of a rational function
Explaining how to find any holes and vertical asymptotes of a rational function
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
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
Solving equations that contain rational expressions
Solving an equation that contains rational expressions
Solving an equation that contains rational expressions
Finding the domain of a piecewise function and evaluating it
Solving an equation with exponential functions
Finding the domain, intercepts, asymptotes, and holes of a rational function
Finding the domain, intercepts, asymptotes, and holes of a rational function
Finding the domain, intercepts, asymptotes, and holes of a rational function
Adding and simplifying rational functions
Computing and simplifying the difference quotient for a rational function
Finding the difference quotient for a quadratic function
Review of limits, continuity, and differentiability
Review of limits at infinity and continuity of functions
Examples of calculating infinite limits with exponentials in a rational function
Review of derivative rules such as product, quotient, and chain rule
Absolute extrema on closed intervals
Factoring rational functions to solve limits
Limits at infinity of rational functions
Determining where functions are continuous
Using the power rule to find derivatives
Examples of Product, Quotient, and Chain Rule
Examples of Product, Quotient, and Chain Rule
Determining concavity and inflection points and sketching the graph
Using Information From the Derivative to Sketch a Graph
Using Critical Values to Find Absolute Extrema on Closed Intervals
Finding Absolute Extrema on Open Intervals
Solving examples finding the area between curves
Finding the area between two curves
Simplifying a fraction using properties of exponents
Simplifying a fraction containing fractional exponents
Simplifying a fraction with negative exponents
Factoring an algebraic expression
Factoring a quadratic
Factoring a polynomial
Factoring a quadratic
Solving a polynomial equation using factoring by grouping
Finding the domains of expressions
Finding the x-intercepts of quadratic functions
Finding properties of a polynomial including zeros and end behavior
Finding properties of a polynomial including zeros and end behavior
Finding properties of a polynomial including zeros and end behavior
Using properties of a polynomial to find its graph
Determining the properties of a rational function and graphing it
Determining the properties of a rational function and graphing it
Solving a nonlinear inequality
Solving a nonlinear inequality
Solving a nonlinear inequality
Solving a nonlinear inequality
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 a trigonometric equation by factoring
Solving a trigonometric equation
Calculating the difference quotient for a rational function
Calculating the difference quotient for a rational function
Review of limits, continuity, and the Intermediate Value Theorem
Review of the limit definition of a derivative and calculating the derivative
Review of limits and derivatives of inverse trigonometric functions
Related rates problems, differentials, linear and quadratic approximations
Review of the limit definition of a derivative and calculating the derivative
Review of limits and derivatives of inverse trigonometric functions
Mean Value Theorem and using derivatives to find the shape of curves
Properties and derivatives of inverse trigonometric functions
Evaluating limits of functions
Evaluating Limits of Functions
Continuity of Functions and the Intermediate Value Theorem
Limits at infinity and asymptotes, along with physics applications
Limits at infinity, asymptotes, and tangent lines
Review of the limit definition of a derivative and calculating the derivative
Differentials, linear approximations and quadratic approximations
Review of the limit definition of a derivative and calculating the derivative
Properties and derivatives of inverse trigonometric functions
Derivatives of exponential and logarithmic functions and the exponential model
Derivatives of exponential and logarithmic functions and the exponential model
Using derivatives to find properties of graphs
Mean Value Theorem and properties of a graph
Mean Value Theorem and properties of a graph
Using derivatives to find properties of graphs
Using Reimann sums and the Fundamental Theorem of Calculus
Using Reimann sums and the Fundamental Theorem of Calculus
Examples of integration by substitution
Finding the vertical and horizontal asymptotes for a rational function
Using the Quotient Rule to differentiate a rational function
Evaluating a limit using L'Hospital's Rule
Evaluating a limit using logarithm properties
Evaluating a limit with an indeterminate difference using a common denominator
Finding the antiderivative of a rational function
Evaluating a a limit from the left for a rational function
Evaluating the limit of a rational function by factoring and cancelling
Using L'Hospital's Rule to evaluate a limit representing a derivative at a point
Evaluating the limit at infinity of a rational function
Evaluating a definite integral by first simplifying the integrand
Examples reviewing integration techniques from Calculus I
Reviewing u-Substitution
Review of partial fractions
Review of partial fractions
Examples of integration by substitution
Examples finding the area bounded by curves
Using the disk, washer, and shell method to find a volume of revolution
Using integrals to solve work problems and find the average value
Using the method of partial fractions to integrate rational functions
Using the method of partial fractions to integrate rational functions
Integrating a rational function using u-substitution
Integrating a rational function using u-substitution
Finding the length of a curve given by parametric equations
Using u-substitution to integrate a rational function
Explaining all four cases of partial fraction decomposition
Using partial fraction decomposition to rewrite and then integrate a rational function
Using partial fraction decomposition to rewrite and then integrate a rational function
Using partial fraction decomposition to rewrite and then integrate a rational function
Using partial fraction decomposition to rewrite and then integrate a rational function
Using partial fraction decomposition to rewrite and then integrate a rational function
Proving a certain parameterization gives the unit circle and showing vector equations of lines are parallel
Using the limit definition to find derivatives of functions and vector functions
Review of limits, continuity, and the Intermediate Value Theorem
Review of the limit definition of a derivative and calculating the derivative
Review of limits and derivatives of inverse trigonometric functions
Related rates problems, differentials, linear and quadratic approximations
Review of the limit definition of a derivative and calculating the derivative
Review of limits and derivatives of inverse trigonometric functions
Mean Value Theorem and using derivatives to find the shape of curves
Properties and derivatives of inverse trigonometric functions
Evaluating limits of functions
Evaluating limits of functions and using the Squeeze Theorem
Proving a piecewise function and a polynomial are continuous
Continuity of Functions and the Intermediate Value Theorem
Limits at infinity and asymptotes, along with physics applications
Using the limit definition to find derivatives of functions and vector functions
Limits at infinity, asymptotes, and tangent lines
Using the limit definition to find derivatives of functions and vector functions
Review of the limit definition of a derivative and calculating the derivative
Differentials, linear approximations, and quadratic approximations
Finding a formula for a higher order derivative and a formula for the second derivative of a product
Review of the limit definition of a derivative and calculating the derivative
Using the Chain Rule to prove facts about derivatives
Finding a formula for a higher order derivative and a formula for the second derivative of a product
Properties and derivatives of inverse trigonometric functions
Derivatives of exponential and logarithmic functions and the exponential model
Using derivatives to find properties of graphs
Mean Value Theorem and properties of a graph
Mean Value Theorem and properties of a graph
Using derivatives to find properties of graphs
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
Reviewing u-Substitution
Review of partial fractions
Review of partial fractions
Examples of integration by substitution
Examples finding the area bounded by curves
Using the disk, washer, and shell method to find a volume of revolution
Using integrals to solve work problems and find the average value
Using integrals to solve work problems and find the average value
Using the method of partial fractions to integrate rational functions
Using the method of partial fractions to integrate rational functions
Finding a partial fraction decomposition and integrating using partial fractions
Determining the domain of a three-dimensional vector function
Finding the domain of a function with a square root in the denominator
Finding the domain of a function with a root and a logarithm 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
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 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
Explaining the general properties of even and odd root functions
How to rewrite radical terms as power terms
Explaining how to solve radical equations and then solving example problems
Solving equations with even roots and checking the solutions
Solving equations with odd radicals
Solving equations with multiple radicals
Properties of exponents applied to power and exponential expressions
Properties of multiplying and simplifying power and exponential expressions
Properties of exponents applied to power and exponential expressions
Properties of exponential growth and decay functions
Properties of the exponential function with base e
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
Simplifying an expression with both power and exponential functions using properties of exponents
Explaining how to solve equations with power and exponential terms
Solving equations with exponential terms
Solving equations with base e exponential terms
Explaining the terminology and rules of logarithms
Explaining the basic properties of logarithmic functions
Expanding logarithmic expressions using logarithm rules
Condensing a logarithmic expression into a single logarithm
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
Explaining all four cases of partial fraction decomposition
Explaining the format and possible solutions for a system of two linear equations