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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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Introduction to Limits
6 videos
Introduction to Limits
An introduction to evaluating limits using graphs, numerical approximation, and substitution
Limits: At Infinity and Infinite
11 videos
Limits: At Infinity and Infinite
Solving limits at infinity and limits that may have infinite behavior
Continuity
5 videos
Continuity
Determining where functions are continuous algebraically and using graphs
Average and Instantaneous Rate of Change
6 videos
Average and Instantaneous Rate of Change
Finding the average and instantaneous rate of change and the slope of secant and tangent lines
Limit Definition of the Derivative
3 videos
Limit Definition of the Derivative
Using the limit definition to find the derivatives of functions
Calculating Derivatives
20 videos
Calculating Derivatives
Finding derivatives of common functions and using the product, quotient and chain rules with several business applications
Implicit Differentiation and Related Rates
6 videos
Implicit Differentiation and Related Rates
Finding derivatives with implicit differentiation and logarithmic differentiation and solving related rates problems
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Analyzing Graphs with Derivatives
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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Absolute Extrema and Optimization
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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Antiderivatives and Integrals
5 videos
Antiderivatives and Integrals
Finding antiderivatives of functions and solving indefinite integrals
Introduction to Limits
These videos are an introduction to evaluating limits using graphs, numerical approximation, and substitution.
Evaluating Limits from a Graph
Evaluating Limits from a Graph
Evaluating One-Sided Limits from a Graph
Evaluating One-Sided Limits from a Graph
Evaluating a Limit Numerically
Evaluating a Limit Numerically
Combinations of Limits from Graphs
Combinations of Limits from Graphs
Evaluating Limits Algebraically
Evaluating Limits Algebraically
Limit of a Piecewise Function
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
Limit of a Rational Function
Limit of a Rational Function (2)
Limit with Multiple Fractions
Limit with Multiple Fractions
Limit of a Fraction with a Square Root
Limit of a Fraction with a Square Root
Limit with an Absolute Value
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
Limit at Negative Infinity of a Rational Function
Limits at Infinity of a Rational Function
Limits at 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
Limits at Infinity of a Fraction with Exponential Functions
Vertical Asymptotes and Holes of a Rational Function
Vertical Asymptotes and Holes of a Rational Function
Horizontal Asymptote of a Fraction with Exponential Functions
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
Where the Graph of a Function is Not Continuous
Continuity of a Function with a Cube Root
Continuity of a Function with a Cube Root
Continuity of a Function with a Square Root and Logarithm
Continuity of a Function with a Square Root and Logarithm
Continuity of a Piecewise Function
Continuity of a Piecewise Function
Solving for a Constant so a Piecewise Function is Continuous
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
Average Rate of Change from a Table
Slope of a Secant Line
Slope of a Secant Line
Instantaneous Rate of Change of a Function
Instantaneous Rate of Change of a Function
Instantaneous Rate of Change of a Rational Function
Instantaneous Rate of Change of a Rational Function
Instantaneous Rate of Change of Profit
Instantaneous Rate of Change of Profit
Slope of a Tangent Line
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 Polynomial Using the Limit Definition
Finding the Derivative of a Rational Function 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
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
Determining Where the Derivative Exists From a Graph
Finding a Derivative with Exponential Functions and Logarithms
Finding a Derivative with Exponential Functions and Logarithms
Finding and Evaluating Derivatives
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 Quotient Rule
Using the Product Rule with a Logarithm
Using the Product Rule with a Logarithm
Using the Product Rule with an Exponential
Using the Product Rule with an Exponential
Using the Quotient Rule on a Rational Function
Using the Quotient Rule on a Rational Function
The Quotient Rule with an Exponential
The Quotient Rule with an Exponential
Using Both the Quotient and Product Rule
Using Both the Quotient and Product Rule
Using the Quotient Rule Twice to Find the Second Derivative
Using the Quotient Rule Twice to Find the Second Derivative
Evaluating Derivatives Using the Product and Quotient Rules
Evaluating Derivatives Using the Product and Quotient Rules
 
Chain Rule
These videos find derivatives using the chain rule.
Using the Chain Rule
Using the Chain Rule
Using the Generalized Exponential Rule
Using the Generalized Exponential Rule
Using Log Properties to Simplify Before Taking the Derivative
Using Log Properties to Simplify Before Taking the Derivative
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
Evaluating Derivatives Using the Chain Rule
Using the Alternate Form of 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
Calculating Marginal Revenue
Finding Marginal Cost and Marginal Average Cost
Finding Marginal Cost and Marginal Average Cost
Calculating Compound Interest
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
Using Implicit Differentiation to Find a Derivative
Using Implicit Differentiation to Find a Derivative (2)
Using Logarithmic Differentiation to Find a Derivative
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 Liquid Filling a Sphere
Solving a Related Rates Word Problem About Profit
Solving a Related Rates Word Problem About Profit
Solving a Related Rates Word Problem About a Sliding Ladder
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 Critical Values
Finding Where a Function is Increasing and Decreasing
Finding Where a Function is Increasing and Decreasing
Increasing and Decreasing and Local Extrema
Increasing and Decreasing and Local Extrema
Increasing and Decreasing and Local Extrema for a Revenue Function
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
Inflection Points and Intervals of Concavity for an Exponential Function
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Inflection Points and Intervals of Concavity from a Graph
Inflection Points and Intervals of Concavity from a Graph
Using the Second Derivative Test to Find Local Extrema
Using the Second Derivative Test to Find Local Extrema
 
NEW! Absolute Extrema and Optimization
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
Local and Absolute Extrema from a Graph
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Absolute Extrema on a Closed Interval
Absolute Extrema on a Closed Interval
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Absolute Extrema on a Closed Interval (2)
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
Maximizing a Product of Numbers
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Finding the Price to Maximize Profit
Finding the Price to Maximize Profit
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Finding the Box with the Largest Volume
Finding the Box with the Largest Volume
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Finding the Box with the Largest Volume
Minimizing the Cost of a Box
 
Antiderivatives
These videos find antiderivatives of functions and solve indefinite integrals. 
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Finding an Antiderivative
Finding an Antiderivative
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Finding an Indefinite Integral
Finding an Indefinite Integral
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Finding an Indefinite Integral with a Fraction
Finding an Indefinite Integral with a Fraction
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Finding a Function from its Derivative and One Value
Finding a Function from its Derivative and One Value
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Finding the Cost Function from Marginal Cost
Finding the Cost Function from Marginal Cost