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Study Guide

MATH 140- Final Exam Guide - Comprehensive Notes for the exam ( 76 pages long!)


Department
Mathematics
Course Code
MATH 140
Professor
Gulick
Study Guide
Final

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UMD
MATH 140
Final EXAM
STUDY GUIDE

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MATH 140 Lecture 1 Precalculus Review and Limits
Solving Equations:
Ex:      
Quadratic Formula:


The quadratic formula is derived from the general formula, which is:
  
Important Functions and Their Graphs:
Polynomial
o Ex:    
o Graph:
Euler’s number e to a power
o Ex:
o Graph:
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Natural Log
o Ex: 
o Graph:
Logarithm
o Ex: 
o Graph:
Trigonometric Functions
o Ex:  , , etc.
o Graphs:
Absolute Value:
o Ex:
o Graph:
Note: When graphing, be sure to label the axes correctly.
Example Problems:
Ex 1:
o      
o Using the product rule:  
o Getting rid of the log using its base:     
o Final answer: 
Ex 2:
o  
   
o Using the definition of cosine:   

o Pythagorean theorem:           
o Final answer:   


Trigonometric Identities:
   
    
Double angle formulas:
o     
o    
Limits:
“Any theorem with a name is important. Denny Gulick
Formal definition of a limit:
o 
   
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