Domain Restrictions
Explaining domain restrictions for denominators, even roots, and logarithms
Domain of Combinations of Functions Video 1
Author: John Fisk
The following problem is solved in this video. It is recommended that you try to solve the problem before watching the video. You can click "Reveal Answer" to see the answer to the problem.
Problem: Find the domain of the function \(f(x)=\dfrac{x}{x-5}+\sqrt{x-1}+\log_5(x+6)\)
Domain: \([1,5)\cup (5,\infty)\)
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WIR 20B M152 V48
Determining if a sequence is increasing, decreasing, or not monotonic and if it is bounded
WIR 20B M152 V56
Using the comparison test to determine if a series converges or diverges
WIR 20B M152 V57
Using the comparison test to determine if a series converges or diverges
WIR 20B M152 V77
Finding a power series representation for a function
WIR 20B M152 V69
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 V85
Converting parametric equations into a Cartesian equation and graphing
MATH 152: Integration by Parts Exercise 4
Solving an indefinite integral with a natural logarithm using integration by parts
MATH 152: Integration by Parts Exercise 5
Solving a definite integral with a natural logarithm using integration by parts
MATH 152: u-Substitution Exercise 3
Using u-substitution to integrate a rational function
MATH 152: u-Substitution Exercise 4
Using u-substitution to evaluate a definite integral with a natural logarithm
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
MATH 152: Improper Integrals Exercise 2
Solving an improper integral where the upper limit of integration is infinity
MATH 152: Improper Integrals Exercise 4
Solving an improper integral where the upper limit of integration is infinity
MATH 152: Improper Integrals Exercise 6
Solving an improper integral where the upper limit of integration is infinity
Vector Functions: MATH 171 Problems 1 & 2
Proving a certain parameterization gives the unit circle and showing vector equations of lines are parallel
Parametric Curves: MATH 151 Problems 1-5
Cartesian equations and parametric equations of curves
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 1-7
Derivatives of exponential functions and the exponential model
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 1 Review Problems 26-35
Review of the limit definition of a derivative and calculating the derivative
Inverse Trigonometric Functions: MATH 171 Problems 4-6
Properties of inverse trig functions and the derivative of arctangent
Limits: MATH 151 Problems 6-20
Evaluating limits of functions
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.
Limits: MATH 151 Problems 6-20
Evaluating limits of functions and using the Squeeze Theorem
Continuity: MATH 171 Problems 6 & 7
Proving a piecewise function and a polynomial are continuous
Approximations and Exponentials: MATH 151 Problems 7-14
Approximation and Newton's Method, and limits and derivatives of exponential functions
Limits and Asymptotes: MATH 151 Problems 7-11
Limits at infinity and asymptotes, along with physics applications
Limits and Asymptotes: MATH 151 Problems 7-11
Limits at infinity, asymptotes, and tangent lines
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
Differentials and Approximations: MATH 151 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
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
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
Approximations and Exponentials: MATH 151 Problems 7-14
Approximation and Newton's Method, and limits and derivatives of exponential functions
Inverse Trigonometric Functions: MATH 171 Problems 4-6
Properties of inverse trig functions and the derivative of arctangent
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
Derivatives of Logarithmic Functions: MATH 171 Problems 1-3
Proving the derivative of ln(x) and the power and product rules using logarithmic differentiation
Mean Value Theorem and Studying the Shape of Curves: MATH 151 Problems 1-6
Mean Value Theorem and properties of a graph
Mean Value Theorem and Studying the Shape of Curves: MATH 151 Problems 1-6
Mean Value Theorem and properties of a graph
L'Hospital's Rule: MATH 171 Problems 7-9
Proving L'Hospital's Rule and using it to evaluate limits
L'Hospital's Rule: MATH 151 Problem 1(a-h)
Using L'Hospital's Rule to solve limits
Riemann Sums: MATH 151 Problems 1-5
Riemann sums, including approximating areas under curves.
Definite Integrals: MATH 171 Problems 5-9
The definition and properties of definite integrals
Integration by Substitution: MATH 171 Problems 4-6
Using u substitution to evaluate integrals and prove facts about logarithms and integrals and
Review for the Common Exam: MATH 152 Exam 1 Review Problems 11-14
Review of work and average value
Review for the Common Exam: MATH 152 Exam 1 Review Problem 36
Review of partial fractions
Review for the Common Exam: MATH 152 Exam 3 Review Problem 6
Review of estimating the sum of a series and the remainder
Review for the Common Exam: MATH 152 Exam 1 Review Problems 34 & 35
Review of partial fractions
Review for the Common Exam: MATH 152 Exam 3 Review Problems 4 & 5
Review of using tests to determine if a series is absolutely convergent, convergent, and divergent
Review for the Common Exam: MATH 152 Exam 3 Review Problem 9
Review of finding the radius and interval of convergence for a power series
Review for the Common Exam: MATH 152 Exam 3 Review Problems 10-13
Review of power series properties and writing functions as power series
Review for the Common Exam: MATH 152 Exam 3 Review Problems 13-18
Review of Taylor and Maclaurin Series and their properties
Review for the Common Exam: MATH 152 Exam 3 Review Problems 19 & 20
Review of Taylor Polynomials and Taylor's Inequality
Review for the Common Exam: MATH 152 Exam 3 Review Problems 4 & 5
Review of using tests to determine if a series is absolutely convergent, convergent, and divergent
Sequences: MATH 152 Problems 1-3
Determining properties of sequences
Taylor Polynomials: MATH 152 Problem 11
Finding a Taylor Polynomial for a function
Representations of Functions as Power Series: MATH 152 Problems 2 & 3
Finding power series representations for functions and the radius and interval of convergence of the power series
Area Between Curves: MATH 152 Problem 1(a-f)
Examples finding the area bounded by curves
Volume (Disks, Washers, and by Slicing): MATH 152 Problems 2 & 3
Examples finding a volume using disks, washers, and by slicing
Volume (the Disk, Washer, and Shell Methods): MATH 152 Problem 1(a-e)
Using the disk, washer, and shell method to find a volume of revolution
Work and Average Value: MATH 152 Problems 1-9
Using integrals to solve work problems and find the average value
Work and Average Value: MATH 152 Problems 1-9
Using integrals to solve work problems and find the average value
Integration by Partial Fractions: MATH 152 Problem 11
Using the method of partial fractions to integrate rational functions
Improper Integrals: MATH 152 Problems 4 & 5
Determining divergence or convergence of improper integrals
WIR2 20B M251 V7
Finding the limit of a three-dimensional vector function
WIR2 20B M251 V8
Finding a vector equation for the tangent line to a three-dimensional vector function
WIR2 20B M251 V12
Finding the position vector function given the velocity and an initial position
WIR3 20B M251 V8
Finding the partial derivatives of a function of two variables
Creating and Manipulating Symbolic Expressions in Python
Creating symbolic expression in Python and then factoring, expanding, and simplifying the expressions
Numerical Calculations in Python
Performing basic numerical calculations in Python
Using Variables in Python
Defining variables in Python and using the variables in equations
Splitting a Domain Into Two Pieces for a Double Integral
Evaluating a double integral over a given region by splitting it into two double integrals
Making Linear Functions Video 1
Discussing how to write the equation of a line through two given points
Making Linear Functions Video 2
Writing a linear equation of profit from a business word problem
Solving Linear Equations Algebraically Video 1
Solving a linear equation algebraically and showing how this relates to the graph
Solving Linear Equations Algebraically Video 2
Solving a linear equation algebraically
Solving Linear Equations Algebraically Video 3
Solving a linear equation algebraically and showing how this relates to the graph
Systems of Two Linear Equations in Two Variables Video 1
Explaining the format and possible solutions for a system of two linear equations
Systems of Two Linear Equations in Two Variables Video 2
Solving a system of linear equations with two variables
Systems of Two Linear Equations in Two Variables Video 3
Solving a system of two linear equations with two variables using the elimination method
Systems of Two Linear Equations in Two Variables Video 4
Solving a system of two linear equations using a TI-84 calculator
Systems of Two Linear Equations in Two Variables Video 5
Solving a system of two linear equations using a TI-84 calculator
Systems of Two Linear Equations in Two Variables Video 6
Solving a system of two linear equations using a TI-84 calculator
Linear Forms Video 1
Explaining the main three forms for linear equations
Quadratic Equations Video 1
Explaining the standard form for a quadratic equation and the possible number of solutions
Quadratic Equations Video 2
Solving quadratic equations with the difference of two squares formula
Quadratic Equations Video 3
Solving quadratic equations by factoring
Quadratic Equations Video 4
Solving a quadratic equation by factoring
Quadratic Equations Video 5
Solving a quadratic equation by factoring
Quadratic Equations Video 6
Solving quadratic equations with the quadratic formula and discussing the number of possible solutions
Quadratic Equations Video 7
Explaining when a quadratic equation does not have a real solution
Properties of Power and Exponential Expressions Video 6
Simplifying power and exponential expressions using properties of exponents
Properties of Power and Exponential Expressions Video 7
Simplifying power and exponential expressions using properties of exponents
Properties of Power and Exponential Expressions Video 8
Simplifying power and exponential expressions using properties of exponents
Properties of Power and Exponential Expressions Video 9
Simplifying an expression with both power and exponential functions using properties of exponents
Properties of Power and Exponential Expressions Video 1
Properties of exponents applied to power and exponential expressions
Properties of Power and Exponential Expressions Video 2
Properties of multiplying and simplifying power and exponential expressions
Properties of Power and Exponential Expressions Video 3
Properties of exponents applied to power and exponential expressions
Properties of Rational Functions and Expressions Video 6
Explaining basic algebraic operations for fractions
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
Functions of Several Variables Exercise V1
Evaluating and then finding and sketching the domain of a function of two variables
Functions of Several Variables Exercise V2
Finding and sketching the domain of a function of two variables
Functions of Several Variables Exercise V4
Sketching the level curves for a function of two variables
Functions of Several Variables Exercise V5
Sketching the level curves for a function of two variables
Cases for Partial Fraction Decomposition
Explaining all four cases of partial fraction decomposition
Finding the nth Taylor Polynomial Exercise
Finding the nth Taylor polynomial of the natural log function centered at 1
Systems of Two Linear Equations in Two Variables Video 1
Explaining the format and possible solutions for a system of two linear equations