How To ... Calculus
Recommended Level: MATH 142
Limits, Derivatives, and Applications of Derivatives
The following videos explain topics you will see in Calculus I, including limits, derivatives, and applications of derivatives. These videos are helpful for any calculus course, but are particularly focused on the concepts and problems seen in MATH 142.
Video Playlists
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6 videos
Introduction to Limits
An introduction to evaluating limits using graphs, numerical approximation, and substitution

11 videos
Limits: At Infinity and Infinite
Solving limits at infinity and limits that may have infinite behavior

5 videos
Continuity
Determining where functions are continuous algebraically and using graphs

6 videos
Average and Instantaneous Rate of Change
Finding the average and instantaneous rate of change and the slope of secant and tangent lines

3 videos
Limit Definition of the Derivative
Using the limit definition to find the derivatives of functions

20 videos
Calculating Derivatives
Finding derivatives of common functions and using the product, quotient and chain rules with several business applications

6 videos
Implicit Differentiation and Related Rates
Finding derivatives with implicit differentiation and logarithmic differentiation and solving related rates problems

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7 videos
Analyzing Graphs with Derivatives
Finding critical values, extrema, and inflection points; finding intervals where the function is increasing or decreasing and concave upward or downward

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7 videos
Absolute Extrema and Optimization
Finding the absolute maximum and minimum on closed intervals; solving word problems by optimizing functions with given constraints

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28 videos
Antiderivatives and Integrals
Finding antiderivatives of functions and solving indefinite integrals including examples using \(u\)substitution; estimating area under curves with Riemann sums; finding the average value of a function; finding the area between curves

Introduction to Limits
These videos are an introduction to evaluating limits using graphs, numerical approximation, and substitution.
Evaluating Limits from a Graph

Evaluating OneSided Limits from a Graph

Evaluating a Limit Numerically

Combinations of Limits from Graphs

Evaluating Limits Algebraically

Limit of a Piecewise Function

Limits: At Infinity and Infinite
These videos solve limits at infinity and limits that may have infinite behavior.
Infinite Limits
These videos contain limits of fractions where the numerator and denominator both approach zero, and the limit may have infinite behavior.
Limit of a Rational Function

Limit of a Rational Function (2)

Limit with Multiple Fractions

Limit of a Fraction with a Square Root

Limit with an Absolute Value

Limits at Infinity
These videos evaluate limits at infinity and negative infinity. They also find horizontal asymptotes, vertical asymptotes, and holes of functions.
Limit at Negative Infinity of a Rational Function

Limits at Infinity of a Rational Function

Limits at Infinity of a Rational Function (2)

Limits at Infinity of a Fraction with Exponential Functions

Vertical Asymptotes and Holes of a Rational Function

Horizontal Asymptote of a Fraction with Exponential Functions

Continuity
These videos determine using graphs and algebraically where functions are continuous. The examples include functions with fractions, even or odd roots, logarithms, and piecewise functions.
Where the Graph of a Function is Not Continuous

Continuity of a Function with a Cube Root

Continuity of a Function with a Square Root and Logarithm

Continuity of a Piecewise Function

Solving for a Constant so a Piecewise Function is Continuous

Average and Instantaneous Rate of Change
These videos find the average and instantaneous rate of change. The videos also include finding the the slope of secant lines and tangent lines of functions.
Average Rate of Change from a Table

Slope of a Secant Line

Instantaneous Rate of Change of a Function

Instantaneous Rate of Change of a Rational Function

Instantaneous Rate of Change of Profit

Slope of a Tangent Line

Limit Definition of the Derivative
These videos use the limit definition to find the derivatives of functions
Finding the Derivative of a Polynomial Using the Limit Definition

Finding the Derivative of a Rational Function Using the Limit Definition

Finding the Derivative of a Root Function Using the Limit Definition

Calculating Derivatives
These videos calculate the derivative of common functions such as polynomials, rational functions, exponential functions, logarithms, and root functions. The videos use derivative rules such as the power rule, product rule, quotient rule, and chain rule.
Finding the Derivative
These videos find the derivative of standard functions such as polynomials, exponential functions, logarithms, and roots. Also, the first video shows how to determine from a graph when the derivative exists.
Determining Where the Derivative Exists From a Graph

Finding a Derivative with Exponential Functions and Logarithms

Finding and Evaluating Derivatives

Product Rule and Quotient Rule
These videos find derivatives using the product rule and quotient rule.
Using the Quotient Rule

Using the Product Rule with a Logarithm

Using the Product Rule with an Exponential

Using the Quotient Rule on a Rational Function

The Quotient Rule with an Exponential

Using Both the Quotient and Product Rule

Using the Quotient Rule Twice to Find the Second Derivative

Evaluating Derivatives Using the Product and Quotient Rules

Chain Rule
These videos find derivatives using the chain rule.
Using the Chain Rule

Using the Generalized Exponential Rule

Using Log Properties to Simplify Before Taking the Derivative

Using Log Properties to Simplify Before Taking the Derivative (2)

Evaluating Derivatives Using the Chain Rule

Using the Alternate Form of the Chain Rule

Business Applications of Derivatives
These videos use derivatives to solve business word problems.
Calculating Marginal Revenue

Finding Marginal Cost and Marginal Average Cost

Calculating Compound Interest

Implicit Differentiation and Related Rates
These videos find the derivative using implicit differentiation and logarithmic differentiation. The videos also use implicit differentiation to solve related rates problems.
Implicit Differentiation and Logarithmic Differentiation
These videos find derivatives using implicit differentiation and logarithmic differentiation. Several videos also show how sometimes you can use logarithmic properties to simplify logarithmic functions before taking the derivative.
Using Implicit Differentiation to Find a Derivative

Using Implicit Differentiation to Find a Derivative (2)

Using Logarithmic Differentiation to Find a Derivative

Related Rates
These videos use implicit differentiation to solve related rates problems.
Solving a Related Rates Word Problem About Liquid Filling a Sphere

Solving a Related Rates Word Problem About Profit

Solving a Related Rates Word Problem About a Sliding Ladder

Analyzing Graphs with Derivatives
Analyzing Graphs with the First Derivative
These videos find the critical values of a function, the intervals where the function is increasing and decreasing, and all local extrema.
Finding Critical Values

Finding Where a Function is Increasing and Decreasing

Increasing and Decreasing and Local Extrema

Increasing and Decreasing and Local Extrema for a Revenue Function

Analyzing Graphs with the Second Derivative
These videos find the inflection points of a function and the intervals of concavity. The videos also cover using the Second Derivative Test to find local extrema.
Inflection Points and Intervals of Concavity for an Exponential Function

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Inflection Points and Intervals of Concavity from a Graph

Using the Second Derivative Test to Find Local Extrema

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Absolute Extrema
These videos find the absolute maximum and absolute minimums of functions. In particular, the videos show how to find the absolute extrema on a closed interval.
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Local and Absolute Extrema from a Graph

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Absolute Extrema on a Closed Interval

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Absolute Extrema on a Closed Interval (2)

Optimization
These videos show how to solve word problems where you need to maximize or minimize a function with given constraints.
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Maximizing a Product of Numbers

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Finding the Price to Maximize Profit

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Finding the Box with the Largest Volume

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Minimizing the Cost of a Box

Antiderivatives and Integrals
Basic Antiderivatives and Integrals
These videos find antiderivatives of functions and solve indefinite integrals.
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Finding an Antiderivative

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Finding an Indefinite Integral

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Finding an Indefinite Integral with a Fraction

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Finding a Function from its Derivative and One Value

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Finding the Cost Function from Marginal Cost

\(u\)Substitution
These videos show how to solve integrals using \(u\)substitution.
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\(u\)Substitution With an Exponential Function

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\(u\)Substitution With a Natural Logarithm

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\(u\)Substitution With a Quotient and Exponentials

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\(u\)Substitution With a Quotient and Root

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Finding the Function from Its Derivative Using \(u\)Substitution

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Calculating Profit From Marginal Profit Using \(u\)Substitution

Area Under Curves and Riemann Sums
These videos show how to calculate the area under curves with geometry and estimate the area with Riemann sums.
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Calculating the Exact Area Under a Curve With Geometry

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Calculating the Exact Area Under a Curve With Geometry (2)

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Introduction to Riemann Sums

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Estimating Area With RightHand Riemann Sums

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Estimating Area With LeftHand Riemann Sums

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Estimating Area With Midpoint Riemann Sums

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Estimating the Area Under a Curve With Riemann Sums

Definite Integrals and the Fundamental Theorem of Calculus
These videos show properties of the definite integral and how to evaluate definite integrals using the Fundamental Theorem of Calculus and antiderivatives.
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Properties of Definite Integrals

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Definite Integral Comparison Properties

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Evaluating a Definite Integral

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Evaluating a Definite Integral (2)

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Evaluating a Definite Integral With \(u\)substitution

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Part 1 of the Fundamental Theorem of Calculus

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Solving a Word Problem With a Definite Integral

Area Between Curves and Average Value of a Function
These videos show how to use definite integrals to find the area between two curves using definite integrals and the average value of a function on an interval.
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Area Between Two Curves on an Interval

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Area of the Region Bounded by Two Curves

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Average Value of a Function on an Interval
