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MAT 145 Study Guide - Midterm Guide: Logarithmic DifferentiationExam

Course Code
MAT 145
Study Guide

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MAT145 Term Test 3
2012 Spring
Part I: Do Not Use Any Calculator or Computer Tools!
Determine the derivative, with respect to x, of each function below. Use appropriate notation for each
derivative and show all required steps.
1.   
2. 
3. 
(Simplify, factor and reduce g’(x), if possible.)
4.       
5. State and correctly spell the first and last names of the two individuals who are credited with
creating calculus more than 300 years ago.
Use the function     for questions 6 through 9. Express all solutions using exact
6. Determine an equation for the tangent line to f when x=-1. Show all appropriate steps to justify
your result and express your equation in the form y=mx+b.
7. Leo was asked about the domain and range of the function f. Leo claimed that the domain
included all real numbers. Explain how you know Leo is correct.
8. Ambrosia created the following limit statements about the function.
a. Circle each TRUE limit statement.
A. 
  
B. 
  
C. 
  
D. 
  
b. Select ONE false limit statement from above and explain how you know it is a false
statement. It is not sufficient to simply state, “The limit is not correct.” Be sure to
indicate which limit statement are you discussing.
9. Zhiangi claims there are no points on the graph of f where the function reaches a maximum or a
minimum. Use your calculus knowledge of functions and their derivatives to support or refute
Zhiangi’s claim. Be clear, precise and specific referring to a calculus-based evidence.
A particle moves along the x axis of a coordinate plane so that its position in relation to the origin, in
centimeters, at time t is
  , t in seconds, t any real number. Use this information for
questions 10 through 14. Please carefully check the units of measure you use with your responses!
10. Calculate the velocity function, v(t), at time t seconds. Include units.
11. Calculate the acceleration function, a(t), at time t seconds. Include units.
12. Determine the instantaneous rate o change of the particle’s position at time t=2 seconds.
Include units.
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