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Math 106 Exam 3: Problem Solving and Calculus, Exams of Advanced Calculus

The august 31, 2006 math 106 exam focusing on problem-solving and calculus concepts, including compound interest, finding maximums and minimums, and integration. Students are required to show their work and partial credit will be given.

Typology: Exams

Pre 2010

Uploaded on 08/16/2009

koofers-user-gio
koofers-user-gio 🇺🇸

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EXAM 3
Math 106
August 31, 2006
Name
You must show all your work. Partial credit will be given.
1. Twenty-five hundred dollars invested in an account that pays 6.4% interest, compounded
quarterly, will generate an amount A= 2500(1.0164t) dollars in tyears.
(a) How much is in the account after three years and what is the rate of change of the
amount in the account at three years? (10 pts)
(b) Using part aestimate the amount you would expect to be in the account after three and
one half years. (Do not use the equation to find an exact amount, use your previous
answers to arrive at an estimate.) (5 pts)
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EXAM 3

Math 106 August 31, 2006

Name

You must show all your work. Partial credit will be given.

  1. Twenty-five hundred dollars invested in an account that pays 6.4% interest, compounded quarterly, will generate an amount A = 2500(1. 0164 t^ ) dollars in t years.

(a) How much is in the account after three years and what is the rate of change of the amount in the account at three years? (10 pts)

(b) Using part a estimate the amount you would expect to be in the account after three and one half years. (Do not use the equation to find an exact amount, use your previous answers to arrive at an estimate.) (5 pts)

  1. For each of the following functions find all relative maximums and/or minimums that exist. (9 pts each)

(a) f (t) = 3 + 5t^3 − 60 t

(b) h(x) = ex

2

  1. The rate of change of annual U.S. factory sales (in billions of dollars per year) for consumer electronic goods to dealers from 1990 to 2001 can be modeled by the equation s(x) = 0. 12 x^2 −
    1. 99 x + 5.7 billion dollars per year where x is the number of years since 1990. Use the idea of a limit of sums to estimate the change in factory sales from 1990 to 2000. Write the definite integral symbol for the exact value of the change in factory sales from 1990 to 2000. (Do not integrate.) (10 pts)
  2. Find each of the following: (6 pts each)

(a)

2 x^3 − 5 x + 3 dx

(b)

7 x −

x

dx

(c)

t^2

  • 2et^ dt

(d)

3 x^ − x^3 dx

(e)

1 3 x

(^2) − 4 x + 3 dx