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MTH 252 Final Exam - Winter Term 2007: Integrals, Limits, and Calculus, Exams of Calculus

Portland Community CollegeCalculus

The final exam for mth 252: calculus, held during the winter term 2007. The exam covers various topics, including integrals, limits, and calculus. Students are required to evaluate integrals and limits, find maximum and minimum values, and perform calculations using a calculator.

Typology: Exams

Pre 2010

Uploaded on 08/16/2009

koofers-user-cxn
koofers-user-cxn 🇺🇸

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MTH 252 Final Exam – No Calc Portion
Winter Term 2007 Name
1. Evaluate each integral. All solutions must be fully substantiated by the work presented on this
paper. (5 points each)
a.
∫
−
2
13
2
328
3
x
dxx
b.
∫
dxex
x7
4
3/23/2007 3:35AM
1 / 6
pf3
pf4
pf5
pf8
pf9

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Download MTH 252 Final Exam - Winter Term 2007: Integrals, Limits, and Calculus and more Exams Calculus in PDF only on Docsity!

MTH 252 Final Exam – No Calc Portion Winter Term 2007 Name

  1. Evaluate each integral. All solutions must be fully substantiated by the work presented on this paper. (5 points each)

a. ∫

2 1 3

2

28 3

x

x dx

b. ∫ 4 x e^7 xdx

3/23/2007 3:35AM 1 / 6

MTH 252 Final Exam – No Calc Portion

c. (^2) 16

x x

e dx

∫ + e

d.

3 0 9 2

θ d θ

3/23/2007 3:37AM 2 / 6

MTH 252 Final Exam – No Calc Portion

3. Find the absolute maximum value of the function f ( x ) = x^3 + 3 x^2 − 9 x + 4 over the interval

[ 0 , 2 ]. All relevant work must be shown on this page in a well-organized and well-documented

manner. (8 points)

4. A certain function, y = g ( ) x , is continuous and differentiable at all points. You are told that

g ′ ( − 2 ) = 0 and that g ′′^ ( ) x = x^4 + x. Which does y = g ( x ) have at x =− 2 : a local

maximum point or a local minimum point? Explain your reasoning! (4 points)

3/23/2007 10:46PM 4 / 6

MTH 252 Final Exam – No Calc Portion

  1. Evaluate

8 3 4 7

dt

t

∞

−

∫ using appropriate analysis and showing all relevant work.^ (8 points)

3/23/2007 3:41AM 5 / 6

MTH 252 Final Exam –Calc Portion Winter Term 2007 Name

Please use your calculator for all calculations on this portion of the test.

1. Consider f ( x ) = x ⋅ 3 x − 4. (14 points total)

a. Find on your calculator thecompletely simplified form of f ′( x ). State the result.

b. State the critical numbers of f. No explanation necessary.

c. Build an increasing/decreasing table for f and then state the local minimum and maximum points on f.

3/23/2007 10:47PM 1 / 3

MTH 252 Final Exam –Calc Portion

  1. The equations of the skew lines in figure 1 and 2 are

y = x + and y = − x − 2.

a. Use an integral (integrals) whose variable is x to find the area of the triangular region in Figure 1. Make sure that you annotate Figure 1 in a manner consistent with that discussed and illustrated in class. (5 points)

b. Use an integral (integrals) whose variable is (^) y to find the area of the triangular region in Figure 2. Make sure that you annotate Figure 1 in a manner consistent with that discussed and illustrated in class. (7 points)

Figure 1

Figure 2

3/23/2007 3:45AM 2 / 3