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 (5)
3)Use SHELL method to find the volume of the solid generated by revolving (5)
4)The base of a solid is the region in the XY-plane bounded by the graph of x² + y² = 16. (5)
5)Find the length of the arc along ( y + 1)² = ( x - 4 )³ (5)
6)Find z such that z satisfies the conditions of the Mean Value Theorem (4)
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C/ Find the limits (Show all your work!)
. (15)
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D/ Evaluate if possible
(12)
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E/ Test for Convergence
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.
obtained by revolving the area bounded by:
y = x2 + 2,
2y - x - 2 = 0,
x = 0,
and x = 1
about the x - axis.
about the Y-axis the region bounded by y = 2x - x² and y = 0 .
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.
from point A (5, 0) to point B (8, 7).
for definite integrals if f(x) = 3x² on the interval from 0 to 3.
(3)
TOTAL (100)
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