MATH 106 PRACTICE
FINAL Please work out each of the given problems. Credit will be based on the steps that you show towards the final answer. Show your work. PROBLEM 1 Evaluate the given integrals, derivatives and limits. A) (20 Points) B)
(20 Points)
C) (20
Points)
D) (20
Points)
E)
(20 Points)
F)
(20 Points)
G) (20
Points)
H) (20 Points) PROBLEM 2 Set up the integrals that solve the following problems. Sketch the appropriate diagram for each. Use a calculator to evaluate the integral. A) (15 Points) Find the volume of solid that is formed by revolving the region bounded by y = x^{2}  4x and y = 2x  5 around the yaxis. B) (15Points) Find the volume of the solid that is formed by revolving the region bounded by y = x^{2} + 1 and y = 5 around the line y = 10 .
PROBLEM 3 (30 Points) A force of 80 Newtons stretches a spring 70 centimeters on a mechanical device for driving fence posts. Find the work done in stretching the spring the required 70 centimeters. PROBLEM 4 (11 Points Each) In 1960 the world population reached 3 billion people and in 1999 the population reached 6 billion people.
PROBLEM 5 (31 Points) Let f(x) = x^{3} + x + 4
PROBLEM
6 Please
answer the following true or false. If
true, provide an explanation. If
false provide an explanation or counterexample. A.
(15 Points) If f(x)
is a continuous positive function then the surface area generated by revolving
the curve y = f(x)
for
0 < x < 1
about the xaxis is equal to the
surface area generated by revolving the curve y
= f(x) + 1 for0 < x < 1
about the xaxis B.
(15 Points) An aquarium has
two exhibits each with vertical windows of the same area such that the bottoms
are at the same depth and the tops are at the same depth.
Then even though the shapes of the two windows may be different, the
fluid forces exerted on the windows are equal.
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