allison blanchard, chris eberz, and jule gamache
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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. Domain and Range. In order for a relation to be a function it must pass the vertical line test. - PowerPoint PPT PresentationTRANSCRIPT
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Final Exam Study GuidePreCalculus Review, L’Hopital’s Rule, Integration By Parts,
Integration by Partial Fractions
Allison Blanchard, Chris Eberz, and Jule Gamache
![Page 2: Allison Blanchard, Chris Eberz, and Jule Gamache](https://reader035.vdocuments.net/reader035/viewer/2022062518/5681401a550346895dab699b/html5/thumbnails/2.jpg)
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
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Examples:
Domain and Range
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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
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Examples:
Function Notation
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More Examples
Function Notation
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More Examples
Function Notation
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This applies function notation by using the arithmetic operations:◦ Addition◦ Subtraction◦ Multiplication◦ Division◦ Substitution (Plugging one into the another)
Operations with Functions
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Examples:
Operations with Functions
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Properties of Exponents
Exponentials and Logarithmic Functions
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Examples:
Exponentials and Logarithmic Functions
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Properties of Logs
Exponentials and Logarithmic Functions
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Examples
Exponentials and Logarithmic Functions
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Solving Equations Using Logs (Examples)
Exponentials and Logarithmic Functions
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Domain and Range Function Notation Operations with Functions Exponentials and Logarithmic Functions
Chapter 1 Quiz!
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L’Hopital’s Rule
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Example
L’Hopital’s Rule
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Integration by Parts
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Examples
Integration by Parts
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More Examples
Integration by Parts
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Integration by Parts More Examples
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More Examples
Integration by Parts
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Rules:
Integration by Partial Fractions
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Decomposition of Fractions Example
Integration by Partial Fractions
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Repeating Linear Fractions Example
Integrations by Partial Fractions
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Shortcut for Non-Repeating Example
Integration by Partial Fractions
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L’Hopital’s Rule Integration by Parts Integration by Partial Fractions
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