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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.
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MTH 252 Final Exam – No Calc Portion Winter Term 2007 Name
2 1 3
2
28 3
x
x dx
3/23/2007 3:35AM 1 / 6
MTH 252 Final Exam – No Calc Portion
c. (^2) 16
x x
e dx
d.
3 0 9 2
θ d θ
3/23/2007 3:37AM 2 / 6
MTH 252 Final Exam – No Calc Portion
manner. (8 points)
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
8 3 4 7
dt
t
∞
−
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.
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
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