Calculus II Final Exam |

This is a 3 hour exam. Graphing Calculators not allowed.

Information(cheat) sheet -- (open in new window) -- click here

Show all your work. Write neatly and large enough to see !!

**A/ Integrate the following**

(30)

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**B/ Make a diagram for questions 1 - 4.**

1) Find the area of the region bounded by *y = 6 - x²* and *y = 3 - 2x* .

(5)

2) Use __DISK__ method to find the volume of the solid

obtained by revolving the area bounded by:

*y = x ^{2} + 2,*

(5)

3)Use __SHELL__ method to find the volume of the solid generated by revolving

about the Y-axis the region bounded by *y = 2x - x**²* and *y = 0* .

(5)

4)The base of a solid is the region in the XY-plane bounded by the graph of *x² + y² = 16*.

Find its volume if every cross section by a plane perpendicular to the X-axis is

an **isosceles triangle** with base on the XY-plane, with** height = the base**.

(5)

5)Find the length of the arc along *( y + 1)² = ( x - 4 )*³

from point **A*** (5, 0)* to point **B*** (8, 7)*.

(5)

6)Find z such that z satisfies the conditions of the Mean Value Theorem

for definite integrals if *f(x) = 3x²* on the interval from 0 to 3.

(4)

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**C/ Find the limits (Show all your work!)**

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(15)

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**D/ Evaluate if possible****
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(12)

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**E/ Test for Convergence****
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1) Test these infinite series. If it converges, find the sum. State the test used.

(8)

2) a) State the 3 requisites for use of the Integral test.

(3)

b) Use the Integral test to prove that the harmonic series, S(1/n) diverges.

(3)

TOTAL (100)

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