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How-To Calculus

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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.

Summary

A review of calculus topics including limits, derivatives, integrals, along with their applications

Sections

Module 1

Limits: Graphically and Numerically Limits: Algebraically Limits: At Infinity and Infinite Continuity from a Calculus Perspective

Module 2

Average and Instantaneous Rates of Change The Limit Definition of the Derivative Introductory Derivative Rules and Marginal Analysis The Product Rule and Quotient Rule The Chain Rule Implicit Differentiation and Related Rates

Module 3

Analyzing Graphs with the First Derivative Analyzing Graphs with the Second Derivative Absolute Extrema Optimization

Module 4

Antiderivatives: Introductory Rules Antiderivatives: Substitution The Definite Integral The Fundamental Theorem of Calculus Average Value of a Function Area Between Two Curves
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