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Name: ________________________ Class: ___________________ Date: __________

ID: A

Study Guide # 1
Numeric Response
1. Find the area of the region bounded by the parabola y = x 2 , the tangent line to this parabola at (1, 1), and the x axis.
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2. Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the specified axis.

y = x 4 , y = 0, y = 1; about the line x = 2
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3. Find the average value of the function on the given interval.
2 È
˘
g(x) = 2xe −x , Í 0, 5 ˙
Í
˙
Î
˚

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4. Find the work done in pushing a car a distance of 9 m while exerting a constant force of 200 N.
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5. A force of 30 N is required to maintain a spring stretched from its natural length of 12 cm to a length of 15 cm. How much work is done in stretching the spring from 12 cm to 18 cm?
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1

Name: ________________________

ID: A

6. Find the volume of the solid obtained by rotating the region bounded by y = 3 x and y = x about the line y = 1.
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7. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. y = lnx, y = 1, y = 3, x = 0; about the y − axis
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8. Find the work done in pushing a car a distance of 12 m while exerting a constant force of 300 N.
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9. The temperature of a metal rod, 8 m long, is 7x (in C °) at a distance x meters from one end of the rod. What is the average temperature of the rod?
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10. Graph the region between the curves and use your calculator to compute the area correct to five decimal places. 2

y = 3e 1 − x , y = 3x 4
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Please Show and Explain each step in order to earn full credit!
2

Name: ________________________

ID: A

11. Find the area of the region bounded by the parabola y = x 2 , the tangent line to this parabola at (10, 100), and the x axis.
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12. Find