AP CALCULUS: COMPREHENSIVE REVIEW OF SECTIONS 5.1 - 5.5

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Chapter 5-I Review

Things to Keep in Mind

The First Fundamental Theorem of Calculus

The Second Fundamental Theorem of Calculus

5.1 Diff’ing with Logs

Logarithm Rules

Derivatives of Natural Logarithms

5.2 Integrating with Logs

If the degree of the numerator  the degree of denominator, divide

Rules to Remember

If  then

If  then   The integral can be calculated knowing

…but don’t forget the chain rule!

Integrals of Trigonometric Functions – Memorize these! (and don’t forget the others!)

5.3 Inverse Functions

f and g are inverses if

f inverse is written as f ^-1

General Rules

If  is continuous ↔ is continuous

If  exists & is not 0 ↔ exists

If  is increasing ↔  is increasing

5.4 Exponential Functions

5.5 Bases Other than e

Changing Bases

Calculating Interest

Let P stand for principle (initial investment)

Let r stand for interest rate (converted from a percent to a decimal)

Let t stand for time

Compounded “n” times:        

Compounded “∞” times:       

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Last modified: 01/09/08