Solving an Inequality with a Sum of Rational Functions
Solving an inequality with two rational expressions using a sign diagram
Problem: Solve the following inequality:\[
\frac{2-x}{x+5} \leq 6
\]
Solving an inequality with two rational expressions using a sign diagram
Solving an inequality with a rational expression using a sign diagram
Adding and then simplifying two rational expressions
Solving an inequality with a polynomial by factoring and using a sign diagram
Solving an inequality with a quadratic by factoring and using a sign diagram
Subtracting rational functions and then simplifying the result
Dividing and subtraction rational functions and simplifying the result
Subtracting rational expressions and simplifying
Performing operations with rational expressions and simplifying
Performing operations with rational expressions and simplifying
Multiplying two rational expressions and then simplifying
Dividing rational expressions and then simplifying the answer
Adding two rational expressions and then simplifying the answer
Simplifying a rational expression
Finding any holes, vertical asymptotes, and horizontal asymptotes of a rational function
Finding any holes, vertical asymptotes, and horizontal asymptotes of a rational function
Matching a rational function with its graph
Finding the domain of a function with a quadratic inside a square root
Computing and simplifying the difference quotient for a rational function
Multiplying two rational functions and simplifying the result
Dividing rational functions and simplifying the result
Adding and simplifying rational functions
Determining the intervals where a function is increasing and decreasing
Dividing rational expressions and simplifying
Solving a nonlinear inequality
Solving a nonlinear inequality
Solving a nonlinear inequality
Solving a nonlinear inequality
Evaluating a limit with an indeterminate difference using a common denominator
Finding the limit of a three-dimensional vector function
Solving a rational equation and checking the solutions
Factoring a quadratic polynomial
Factoring a quadratic function
Factoring a cubic polynomial by grouping
Finding the greatest common factor of a polynomial and then factoring it out
Factoring a quadratic where the leading coefficient is 1
Factoring quadratics where the leading coefficient is not 1
Factoring several polynomials by grouping
Factoring a difference of two squares
Factoring a sum of cubes and a difference of cubes
Finding the roots of a square root function
Finding the domain of a rational function
Finding the domain of a rational function
Finding the composition of a rational function and a quadratic
Finding the inverse of a rational function and its domain
Finding the inverse of a rational function and its domain
Finding and simplifying the difference quotient for a rational function
Finding and simplifying the difference quotient for a square root function
Solving an equation with exponential functions by factoring
Solving a equation with exponential functions by factoring
Solving an quadratic-like equation with sine by factoring
Creating symbolic expression in Python and then factoring, expanding, and simplifying the expressions
Finding the domain of a rational function using factoring
Performing algebraic operations with rational expressions and simplifying the answer
How to simplify rational expressions
Adding and subtracting rational expressions by finding a common denominator
Solving equations that contain rational expressions
Solving an equation that contains rational expressions
Solving an equation that contains rational expressions
Explaining how to graph linear inequalities
Graphing two linear inequalities
Sketching the solution set and finding the corner points for a system of linear inequalities
Graphing the solution set of an inequality with two variables
Graphing the solution set of an inequality with two variables
Graphing the solution set of system of linear inequalities
Finding the domain of a piecewise function and evaluating it
Solving an equation with exponential functions
Finding the difference quotient for a quadratic function
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
Finding the limit of a rational function algebraically
Finding the limit of a rational function algebraically
Solving a limit approaching negative infinity for a rational function
Solving the limits approaching infinity and negative infinity of a rational function
Solving the limits approaching infinity and negative infinity of a rational function
Finding the holes and vertical asymptotes of a rational function
Finding the exact value of the instantaneous rate of change
Using the limit definition to find the derivative of a rational function
Finding the derivative of a rational function by simplifying and using the power rule
Finding the derivative of a rational function using the Quotient Rule
Using the quotient rule twice to find the second derivative of a rational function
Finding the absolute maximum and minimum of a rational function on two closed intervals
Factoring an algebraic expression
Factoring a quadratic
Factoring a polynomial
Factoring a quadratic
Calculating the difference quotient for a rational function
Calculating the difference quotient for a rational function
Solving a linear inequality and graphing the solution set
Solving a linear inequality and graphing the solution set
Solving an inequality with an absolute value and graph its solution set
Solving an inequality with an absolute value
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 an equation with exponential functions by factoring
Solving a trigonometric equation by factoring
Solving a trigonometric equation
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 Riemann 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
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
Reviewing u-Substitution
Review of partial fractions
Review of partial fractions
Finding the length of a curve given by parametric equations
Integrating a rational function using u-substitution
Integrating a rational function using u-substitution
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
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
Proving a piecewise function and a polynomial are continuous
Limits at infinity and asymptotes, along with physics applications
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
Review of the limit definition of a derivative and calculating the derivative
Finding a formula for a higher order derivative and a formula for the second derivative of a product
Using the Chain Rule to prove facts about derivatives
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 Riemann sums and the Fundamental Theorem of Calculus
Examples of integration by substitution
Reviewing u-Substitution
Review of partial fractions
Review of partial fractions
Finding a partial fraction decomposition and integrating using partial fractions
Explaining all four cases of partial fraction decomposition
Determining the domain of a three-dimensional vector function
Explaining all four cases of partial fraction decomposition
Finding all solutions to a trigonometric equation with sine
Solving a trigonometric equation with sine and cosine by factoring
Solving a trigonometric equation with secant by factoring
Solving a trigonometric equation with tangent and sine by factoring
Solving a trig equation with sine and cosine using aPythagorean Identity
Solving an equation with logarithmic functions
Solving an equation with logarithmic functions
Solving an equation with logarithmic functions
Finding the domain, intercepts, holes, and vertical asymptotes for a rational function
Compute and simplify the difference quotient for a rational function
Writing the equation of a line passing through two points
Writing the equation of a line through two points in slope-intercept form
Writing the equation of a graphed line in standard form
Using the quadratic formula to find the roots of a function
Finding the roots of a cubic polynomial
Finding the roots of a function with an absolute value
Finding the domain of a function with a fraction and radicals
Finding the composition of two functions
Finding the composition of two functions with exponentials and logarithms
Finding the composition of two functions with a square root and a fractional exponent
Finding the composition of two functions with a cube root and a fractional exponent
Finding the inverse of a linear function and its domain
Finding the inverse of a square root function and its domain
Finding and simplifying the difference quotient for a quadratic function
Finding the absolute maximum or absolute minimum of a quadratic
Writing the standard form of quadratic function given its vertex and one other point
Finding the component form and magnitude for a vector between two points
Performing calculations with vectors including addition, subtraction, and scalar multiplication
Calculating the dot product for three pairs of vectors
Finding a unit vector in the direction of a given vector
Solving a system of two linear equations using the method of substitution
Solving a system of two linear equations using the method of substitution
Solving a system of two linear equations
Solving a system on two equations where one is linear and one is quadratic
Solving a equation with an exponential function
Solving an equation with two exponential functions with different bases
Finding the size of a population of rabbits with exponential growth
Finding the size of a population of rabbits with exponential decay
Finding the horizontal asymptote of an exponential function
Finding the horizontal asymptote of an exponential function
Finding the horizontal asymptote of an exponential function
Expanding a logarithmic expression using logarithm properties
Condensing logarithmic expressions into a single logarithm
Finding the exact value of logarithms using logarithmic properties
Finding the vertical asymptote of a logarithmic function
Finding the vertical asymptote of a logarithmic function
Finding the domain and x-intercepts of a logarithmic function
Finding the domain and x-intercepts of a logarithmic function
Solving a logarithmic equation using properties of logarithms
Solving a logarithmic equation using properties of logarithms
Finding the values of all six trigonometric functions of an angle given a right triangle
Evaluating the other five trigonometric functions for an acute angle given the value of sine
Evaluating the other five trigonometric functions given sine and that tangent is negative
Finding the solutions to an equation with tangent in a given interval
Solving a trigonometric equation with sine and cosine on a given interval
Solving an equation with cosine on a given interval
Solving a trigonometric equation with sine on a given interval
Sketching one period of a transformed sine graph
Sketching one period of a cosine function with transformations
Finding the amplitude, period, phase shift, and vertical shift for a given sine function
Writing a cosine function for a given graph
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 function with a denominator, square root, and logarithm
Finding the domain of a function with a natural logarithm and denominator
Solving a linear equation algebraically
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
Finding horizontal asymptotes for rational functions
Determining the end behavior and horizontal asymptotes for rational functions
Explaining basic algebraic operations for fractions
Explaining how to do polynomial long division
Explaining how to multiply and divide rational expressions
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