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Final Exam Study Guide PreCalculus Review, L’Hopital’s Rule, Integration By Parts, Integration by Partial Fractions Allison Blanchard, Chris Eberz, and Jule Gamache
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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