Final Exam Study GuidePreCalculus Review, L’Hopital’s Rule, Integration By Parts,

Integration by Partial Fractions

Allison Blanchard, Chris Eberz, and Jule Gamache

In order for a relation to be a function it must pass the vertical line test.

Inverse of a function must pass the horizontal line test.

In order to be included in the domain of a function, the values must not make the denominator equal zero.

We can also only have nonnegative values in an even root.

Domain and Range

Examples:

Domain and Range

For each function there is a set: one domain value corresponds with one range value.

Function Notation sets up an equation that allows one to easily find a range value by inputting a domain value.

Function Notation

f∘g f∙g

Examples:

Function Notation

More Examples

Function Notation

More Examples

Function Notation

This applies function notation by using the arithmetic operations:◦ Addition◦ Subtraction◦ Multiplication◦ Division◦ Substitution (Plugging one into the another)

Operations with Functions

Examples:

Operations with Functions

Properties of Exponents

Exponentials and Logarithmic Functions

Examples:

Exponentials and Logarithmic Functions

Properties of Logs

Exponentials and Logarithmic Functions

Examples

Exponentials and Logarithmic Functions

Solving Equations Using Logs (Examples)

Exponentials and Logarithmic Functions

Domain and Range Function Notation Operations with Functions Exponentials and Logarithmic Functions

Chapter 1 Quiz!

L’Hopital’s Rule

Example

L’Hopital’s Rule

Integration by Parts

Examples

Integration by Parts

More Examples

Integration by Parts

Integration by Parts More Examples

More Examples

Integration by Parts

Rules:

Integration by Partial Fractions

Decomposition of Fractions Example

Integration by Partial Fractions

Repeating Linear Fractions Example

Integrations by Partial Fractions

Shortcut for Non-Repeating Example

Integration by Partial Fractions

L’Hopital’s Rule Integration by Parts Integration by Partial Fractions

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