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Calculus II - Spring 2009 Exam Solutions for Math 121 - Prof. David E. Joyce, Exams of Calculus

The solutions to the calculus ii final exam for math 121 held in spring 2009. The exam covers various topics such as acceleration, integration, and derivatives.

Typology: Exams

Pre 2010

Uploaded on 08/07/2009

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Math 121 Calculus II Spring 2009
Prob Pts
1
2
3
4
5
6
Total
Final Exam Name: (print neatly)
Instructor: Joyce Servatius (sign)
1. (12 pts) Suppose a point moves along the x-axis with acceleration a(t) = e3t
e3t
2
meters per second squared. If the point starts at the origin with velocity 30 meters per
second, what is it’s position 5 seconds later.
2. (16 pts) Suppose Z2
0
(2f(x)+3g(x)) dx = 5 and Z2
0
(5f(x)+2g(x)) dx = 4.
a) Find Z2
0
(f(x)g(x)) dx.
b) What is the average value of f(x) on the interval [0,2].
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Math 121 Calculus II Spring 2009

Prob Pts

Total

Final Exam Name: (print neatly) Instructor: Joyce Servatius (sign)

  1. (12 pts) Suppose a point moves along the x-axis with acceleration a(t) =

e^3 t^ − e−^3 t 2 meters per second squared. If the point starts at the origin with velocity 30 meters per second, what is it’s position 5 seconds later.

  1. (16 pts) Suppose

∫ (^2) 0

(2f (x) + 3g(x)) dx = 5 and

∫ (^2) 0

(5f (x) + 2g(x)) dx = 4.

a) Find

∫ (^2) 0

(f (x) − g(x)) dx.

b) What is the average value of f (x) on the interval [0, 2].

  1. (12 pts) Find the area bounded by the curves y = 0, 3x + 2y = 6 and 3x + y^2 = 9.

-2 -1 1

y 6 J J J J J J J J

JJ

x

  1. (16 pts.) Evaluate the following derivatives.

a. d dx

( e^3 x (^2) + ln(3x^2 + 2)

)

b. d dx

[ arctan(x) 1 + x^2

]

c. d dx

[ 1 + ln(x) x

]

  1. (32 pts.) Compute the following integrals:

a)

∫ (e^2 )1+x^ dx

b)

∫ (^ sin(3x) 3 + cos(3x)

) dx

Intentionally Blank Area. Use for scrap work. You may write on the reverse if you need more room.

Intentionally Blank Area. Use for scrap work. You may write on the reverse if you need more room.