 # 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
Click the playlist you are interested in to go straight to those videos. Or you can scroll down through the page to look through all the videos yourself. 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 NEW! 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 NEW! 7 videos Absolute Extrema and Optimization Finding the absolute maximum and minimum on closed intervals; solving word problems by optimizing functions with given constraints NEW! 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 One-Sided 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

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 NEW! Inflection Points and Intervals of Concavity from a Graph 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.
 NEW! Local and Absolute Extrema from a Graph NEW! Absolute Extrema on a Closed Interval NEW! 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.
 NEW! Maximizing a Product of Numbers NEW! Finding the Price to Maximize Profit NEW! Finding the Box with the Largest Volume NEW! Minimizing the Cost of a Box

Antiderivatives
These videos find antiderivatives of functions and solve indefinite integrals.
 NEW! Finding an Antiderivative NEW! Finding an Indefinite Integral NEW! Finding an Indefinite Integral with a Fraction NEW! Finding a Function from its Derivative and One Value NEW! Finding the Cost Function from Marginal Cost