Math 132 - Christian Brothers University
Math 132 Test 1 Sec. 4.5-4.8 Carter Name_________________________
Show all work in order to receive credit. Numbers at right indicate point value.
Calculator-Free
1. Evaluate the integrals. (7 each)
a. [pic] b. [pic]
c. [pic] d. [pic]
e. [pic] f. [pic]
2. Find the derivative of the following with respect to x. (7 each)
a) [pic]
b) [pic]
3. If [pic] (6)
4. Find the equation of the line tangent to [pic] at x = 1. (10)
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Math 132 Test 1 Carter Name_______________________
Show all work in order to receive credit.
Part II: Calculator-allowed
5. Use the trapezoid rule & midpoint rule with n = 20 to approximate[pic]. Show all of your steps. Write the summation formula before using the calculator. (14)
6. The data gives the measurements in meters of the width of a plot of land. The measurements are taken at100 meter intervals. Use the trapezoid rule and Simpson’s rule to estimate the area of the plot. (14)
x |0 |100 |200 |300 |400 |500 |600 |700 |800 |900 |1000 | |y |125 |125 |120 |112 |90 |90 |95 |88 |75 |50 |35 | |
Answers: check #1 w/ calculator, don’t forget “+C” for indefinite integrals
2. F’(x) = [pic]; dy/dx = 5/x + cot x – tan x; 3) 4; 4) y = 0.5x – 0.5
5. MPS = 2.57699 Trap = 2.57756; 6. Trap = 92,500 Simpson’s = 92,666.67
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