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Where the Graph of a Function is Not Continuous

Determining where a piecewise function is continuous from its graph

Continuity of a Piecewise Function

Determining where a piecewise function is continuous algebraically

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 14-25

Review of limits, continuity, and the Intermediate Value Theorem

MATH 140 5.5 Exercise 4

Writing an absolute value function as a piecewise-defined function

Evaluating Limits from a Graph

Finding limits from the graph of a piecewise function

Limit of a Piecewise Function

Finding one and two-sided limits for a piecewise function algebraically

Limit with an Absolute Value

Finding the limit algebraically of a function with an absolute value

Continuity of a Function with a Cube Root

Finding where a function with a fraction and cube root is continuous

Continuity of a Function with a Square Root and Logarithm

Determining where a function with a fraction, square root, and logarithm is continuous

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 1 Review Problems 26-35

Review of the limit definition of a derivative and calculating the derivative

Limits: MATH 151 Problems 6-20

Evaluating limits of functions

Limits: MATH 151 Problems 6-20

Evaluating Limits of Functions

Continuity: MATH 151 2.5 Problems 1-6

Continuity of Functions and the Intermediate Value Theorem

Review for the Common Exam: MATH 151 3.1 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 3.2 Exam 1 Review Problems 26-35

Review of the limit definition of a derivative and calculating the derivative

Studying the Shape of Curves: MATH 151 4.1 Problems 2-7

Using derivatives to find properties of graphs

Studying the Shape of Curves: MATH 151 Problems 2-7

Using derivatives to find properties of graphs

MLC WIR 20B M151 week2 #10

Explaining why a piecewise function is discontinuous at a point

MLC WIR 20B M151 week2 #11

Solving for the values for constants to make a piecewise function is continuous

MLC WIR 20B M151 week6 #16

Solving for constants so that a piecewise function is differentiable everywhere

MLC WIR 20B M151 week10 #7

Solving for a constant so that a piecewise function is continuous

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

Limits: MATH 151 Problems 6-20

Evaluating limits of functions

Limits: MATH 151 Problems 6-20

Evaluating Limits of Functions

Continuity: MATH 151 2.5 Problems 1-6

Continuity of Functions and the Intermediate Value Theorem

Continuity: MATH 171 Problems 6 & 7

Proving a piecewise function and a polynomial are continuous

Differentiation Formulas: MATH 171 Problems 4 & 5

Using the limit definition to find a derivative and proving the power rule

Review for the Common Exam: MATH 151 3.1 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 3.2 Exam 1 Review Problems 26-35

Review of the limit definition of a derivative and calculating the derivative

Studying the Shape of Curves: MATH 151 4.1 Problems 2-7

Using derivatives to find properties of graphs

Studying the Shape of Curves: MATH 151 Problems 2-7

Using derivatives to find properties of graphs

Continuous Functions of Two Variables Example 2

Determining if a piecewise function of two variables is continuous at a point

Math 140 Exam 3 Review Exercise 3

Writing an absolute value function as an equivalent, piecewise-defined function

Math 140 Exam 3 Review Exercise 9

Finding the domain of a piecewise-defined function and evaluating it for given x-values

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

MATH 140 2.2 Exercise 1

Writing a function for the value of an item depreciating linearly over time

MATH 140 Exam 1 Review #3

Writing a linear function representing the depreciation of a car

MATH 140 5.5 Exercise 5

Writing a piecewise-defined function for a word problem

MATH 140 5.5 Exercise 1

Finding the domain of a piecewise function and evaluating it

MATH 140 5.5 Exercise 2

Finding the piecewise-defined function for a given graph along with its domain and range

MATH 140 5.5 Exercise 3

Graphing a piecewise function

MATH 140 5.7 Exercise 8

Evaluating compositions of two given functions and the graph of a third function

Evaluating One-Sided Limits from a Graph

Finding one-sided limits from the graph of a piecewise function

Evaluating a Limit Numerically

Finding the limit of a function numerically using a calculator

Combinations of Limits from Graphs

Finding limits of combinations of functions using their graphs

Evaluating Limits Algebraically

Using the properties of limits to find several limits algebraically

Limit of a Rational Function

Finding the limit of a rational function algebraically

Limit of a Rational Function 2

Finding the limit of a rational function algebraically

Limit with Multiple Fractions

Finding the limit algebraically of a function with multiple fractions

Limit of a Fraction with a Square Root

Finding the limit algebraically of a function with a square root in the numerator of a fraction

Limit at Negative Infinity of a Rational Function

Solving a limit approaching negative infinity for a rational function

Limits at Infinity of a Rational Function

Solving the limits approaching infinity and negative infinity of a rational function

Limits at Infinity of a Rational Function 2

Solving the limits approaching infinity and negative infinity of a rational function

Limits at Infinity of a Fraction with Exponential Functions

Solving the limits approaching infinity and negative infinity with exponential functions in the numerator and denominator

Vertical Asymptotes and Holes of a Rational Function

Finding the holes and vertical asymptotes of a rational function

Horizontal Asymptote of a Fraction with Exponential Functions

Finding the horizontal asymptotes of a function that is a fraction with exponentials in the numerator and denominator

Average Rate of Change from a Table

Finding the average rate of change over time periods from a table

Slope of a Secant Line

Finding the slope of a secant line to a given function

Instantaneous Rate of Change of a Function

Finding the exact value of the instantaneous rate of change

Instantaneous Rate of Change of a Rational Function

Finding the exact value of the instantaneous rate of change

Instantaneous Rate of Change of Profit

Finding the instantaneous rate of change of profit for a given price-demand function and cost function

Slope of a Tangent Line

Finding the equation of the tangent line to a function using the limit definition

Finding the Derivative of a Polynomial Using the Limit Definition

Using the limit definition to find the derivative of a polynomial

Finding the Derivative of a Rational Function Using the Limit Definition

Using the limit definition to find the derivative of a rational function

Finding the Derivative of a Root Function Using the Limit Definition

Using the limit definition to find the derivative of a square root function

Determining Where the Derivative Exists From a Graph

Determining where the derivative of a function does not exist from a graph

Finding a Derivative with Exponential Functions and Logarithms

Finding the derivative a function with a power, exponential, and logarithm

Finding a Derivative by Simplifying a Rational

Finding the derivative of a rational function by simplifying and using the power rule

Evaluating Derivatives From a Given Table

Finding and evaluating derivatives using values given in a table

Calculating Marginal Revenue

Finding the marginal revenue given the price-demand function for a word problem

Using the Product Rule with a Logarithm

Finding a derivative of a function with a logarithm using the Product Rule

Using the Product Rule with an Exponential

Finding the derivative of a function with a square root and exponential using the Product Rule

The Quotient Rule with an Exponential

Finding the derivative of a fraction with an exponential using the Quotient Rule

Using Both the Quotient and Product Rule

Finding a derivative using both the Product and Quotient Rule

Using the Product and Quotient Rules with a Table

Finding a derivative using the Product and Quotient Rule and values given in a table

Using the Generalized Power Rule

Finding the derivative of a function using the Generalized Power Rule

Using the Generalized Exponential Rule

Using the Generalized Exponential Rule to find the derivative of a function

Using Log Properties to Simplify Before Taking the Derivative

Using logarithm properties to simplify before using the Chain Rule to find a derivative

Using Log Properties to Simplify Before Taking the Derivative 2

Using logarithm properties to simplify before using the Generalized Logarithm Rule to find a derivative

Using the Chain Rule with a Table

Using the chain rule to find derivates with some values given in a table

Calculating the Rate of Growth With Compound Interest

Finding the rate a balance is increasing for interest compounded monthly and continuously

Using the Alternate Form of the Chain Rule

Using the alternate form of the Chain Rule to find the derivative

Using Logarithmic Differentiation to Find a Derivative

Finding the derivative of a function that requires logarithmic differentiation

Using Implicit Differentiation to Find a Derivative

Using implicit differentiation to find the derivative of a function

Using Implicit Differentiation to Find a Derivative 2

Using implicit differentiation to find the derivative of a function

Solving a Related Rates Word Problem About Liquid Filling a Sphere

Finding the rate water is flowing into an expandable sphere given the rate a sphere is growing

Solving a Related Rates Word Problem About Profit

Finding the rate of change of profit given the rate of increase for sales

Solving a Related Rates Word Problem About a Sliding Ladder

Finding how fast a ladder moves up a wall as the bottom is being pushed

Finding Critical Values

Finding the critical values for several functions

Finding Where a Function is Increasing and Decreasing

Determining the intervals where a function is increasing and decreasing

Increasing and Decreasing and Local Extrema

Finding the intervals where a function is increasing/decreasing and the local extrema

Increasing and Decreasing and Local Extrema for a Revenue Function

Finding intervals of increase/decrease and the local extema for revenue from a word problem

Using the Quotient Rule Twice to Find the Second Derivative

Using the quotient rule twice to find the second derivative of a rational function

Inflection Points and Intervals of Concavity for an Exponential Function

Finding the intervals of concavity and inflection points for a function with exponentials

Inflection Points and Intervals of Concavity from a Graph

Determining the intervals of concavity and inflection points from the graph of a function

Local and Absolute Extrema from a Graph

Finding all local and absolute extrema of a function from a graph

Absolute Extrema on a Closed Interval

Finding the absolute maximum and minimum of a rational function on two closed intervals

Absolute Extrema on a Closed Interval 2

Finding the absolute maximum and absolute minimum of a rational function on two closed intervals

Maximizing a Product of Numbers

Finding the maximum product of two numbers given their sum is 100

Finding the Price to Maximize Profit

Finding the selling price of trucks to maximize profit given the cost and price-demand functions

Finding the Box with the Largest Volume

Finding the dimensions of the box with the largest volume given the amount of material to make the box

Minimizing the Cost of a Box

Finding the minimum cost of a box given the volume and cost of materials

Finding an Antiderivative

Finding the antiderivative of a function

Finding an Indefinite Integral

Evaluating an indefinite integral with an exponential

Finding an Indefinite Integral with a Fraction

Solving an indefinite integral by first simplifying the fraction

Finding a Function from its Derivative and One Value

Solving for a function given its derivate and one value

Finding the Cost Function from Marginal Cost

Solving the antiderivative of marginal cost to find the cost function and evaluating a particular cost

u-Substitution With an Exponential Function

Solving an indefinite integral with an exponential function suing u-substitution

u-Substitution With a Natural Logarithm

Solving an indefinite integral with a natural logarithm using u-substitution

u-Substitution With a Quotient and Exponentials

Solving an indefinite integral with exponentials in a quotient using u-substitution

u-Substitution With a Quotient and a Root

Solving an indefinite integral with a cube root in the denominator using u-substitution

Finding the Function from Its Derivative Using u-Substitution

Using u-substitution in an indefinite integral to find a function from its derivative and a given vaue

Calculating Profit From Marginal Profit Using u-Substitution

Calculating profit from marginal profit using an indefinite integral and u-substitution

Calculating the Exact Area Under a Curve With Geometry

Using geometric formulas for circles, triangles, and rectangles to find the exact area under a curve

Introduction to Riemann Sums

Estimating the area under a function using right-hand, left-hand, and midpoint Riemann sums

Estimating Area With a Right-Hand Riemann Sum

Estimating the area under a curve using right-hand Riemann sums

Estimating Area With a Left-Hand Riemann Sum

Estimating the area under a curve using left-hand Riemann sums

Estimating Area With a Midpoint Riemann Sum

Estimating the area under a curve using midpoint Riemann sums

Estimating the Area Under a Curve With a Riemann Sum

Estimating the area under a graph using right-hand Riemann sums

Calculating a Definite Integral From a Graph

Calculating a definite integral by finding the area under a curve using geometry

Definite Integral Comparison Properties

Comparing two definite integrals with the same limits of integration

Evaluating a Definite Integral

Using the Fundamental Theorem of Calculus to evaluate a definite integral

Evaluating a Definite Integral 2

Using the Fundamental Theorem of Calculus to evaluate a definite integral

Evaluating a Definite Integral with u-Substitution

Using the Fundamental Theorem of Calculus and \(u\)-substitution to evaluate a definite integral

Part 1 of the Fundamental Theorem of Calculus

Using Part 1 of the Fundamental Theorem of Calculus to find the derivative of a function defined using an integral

Solving a Word Problem With a Definite Integral

Solving a word problem using a definite integral and the Fundamental Theorem of Calculus

Average Value of a Function

Finding the average value of a a function on an interval using a definite integral

Area Between Two Curves

Finding the area between two curves on an interval using a definite integral

Area of the Region Bounded by Two Curves

Finding the area of a region bounded by two curves using definite integrals

WIR1 20B M150 V9

Simplifying an expression with radicals

WIR1 20B M150 V6

Solving an inequality with an absolute value and graph its solution set

WIR8 20B M150 V06

Solving an inequality with an absolute value

WIR2 20B M150 V9

Evaluating a piecewise function

Vectors: MATH 151 J.1 Problems 1 & 2

Basic Vector Operations such as Addition, Subtraction, and Scalar Multiplication

Review for the Common Exam: MATH 151 Exam 3 Review Problems 1-7

Derivatives of exponential functions and the exponential model

Riemann Sums and Definite Integrals: MATH 151 5.2 Problems 6-12

Using Reimann sums and the Fundamental Theorem of Calculus

Riemann Sums and Definite Integrals: MATH 151 5.3 Problems 6-12

Using Riemann sums and the Fundamental Theorem of Calculus

MLC WIR 20B M151 week2 #08

Evaluating left and right limits of a fraction containing an absolute value

MLC WIR 20B M151 week2 #09

Evaluating one-sided and two-sided limits of a piecewise

MLC WIR 20B M151 week3 #18

Solving for the value of a constant that makes a function is continuous everywhere

MLC WIR 20B M151 week10 #17

Finding the value for a function that satisfies the Mean Value Theorem on an interval

Vectors: MATH 171 Problems 1 & 2

Proving associative and scalar multiplication properties for vectors

Vectors: MATH 151 J.1 Problems 1 & 2

Basic Vector Operations such as Addition, Subtraction, and Scalar Multiplication

Review for the Common Exam: MATH 151 Exam 3 Review Problems 1-7

Derivatives of exponential functions and the exponential model

Limits: MATH 171 Problem 7

Proving a property for limits of sums using the epsilon-delta definition

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.

Precise Definition of a Limit: MATH 171 Problems 3 & 4

Proving limits using the epsilon-delta definition

Precise Definition of a Limit: MATH 171 Problems 5 & 6

Proving limits using the epsilon-delta definition

Continuity: MATH 171 Problems 8 & 9

Proving a product of continuous functions is continuous and using the Intermediate Value Theorem

Trigonometry Derivatives and the Chain Rule: MATH 171 Problems 1-3

Proving the derivatives of trigonometric functions and that sine is continuous

L'Hospital's Rule: MATH 171 Problems 7-9

Proving L'Hospital's Rule and using it to evaluate limits

Riemann Sums and Definite Integrals: MATH 151 5.2 Problems 6-12

Using Reimann sums and the Fundamental Theorem of Calculus

Riemann Sums and Definite Integrals: MATH 151 5.3 Problems 6-12

Using Riemann sums and the Fundamental Theorem of Calculus

Fundamental Theorem of Calculus: MATH 171 Problems 1-3

Proving and then applying the Fundamental Theorem of Calculus

Cumulative Distribution Function Video 2

Explaining the properties of a cumulative distribution function for a random variable

Cumulative Distribution Function Exercise 2

Finding the cumulative distribution function for a random variable from its probability distribution function

Continuous Functions of Two Variables Example 1

Determining if a piecewise function of two variables is continuous

Math 140 Exam 3 Review Exercise 14

Writing the equations for given parent functions and a list of transformations

Math 140 Exam 3 Review Exercise 16

Writing a piecewise-defined function for the late fees charged by a library

Roots of a Function with an Absolute Value

Finding the roots of a function with an absolute value

A Composition of Tangent and Arccosine

Evaluating a composition of tangent and arccosine

Plotting Multiple Expressions in One Graph in Python

Graphing a piecewise function using Python

Cumulative Distribution Function Video 2

Explaining the properties of a cumulative distribution function for a random variable

Cumulative Distribution Function Exercise 2

Finding the cumulative distribution function for a random variable from its probability distribution function

Introduction to Riemann Sums

Estimating the area under a function using right-hand, left-hand, and midpoint Riemann sums