Calculus II 
Final Exam

May 23, 2002

Name____________________ 
R. Hammack

Score______

(1) Evaluate the following integrals.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(2) Evaluate the following definite integrals
(a)
(b)
(c)
(3) Evaluate the following integrals.
(a)
(b)
(4) Evaluate the following definite integrals. (Notice that they are
both improper.)
(a)
(b)
(5) Consider the region between the graph of
and the xaxis.
(a) This region is rotated around the yaxis. What is the volume
of the resulting solid?
(b) This region is rotated around the xaxis. What is the volume
of the resulting solid?
(6) Find the area enclosed between the curves , , , and x = 1.
(7) Find the derivative of the function
(8) Decide if the following sequences converge or diverge. In the case of convergence, find the limit.
(a)
(b)
(9) Decide if the following series converge or diverge.
(a)
(b)
(c)
(d)
(10) Both of the following series converge. Say what number
they converge to.
(a) ]
(b)
(11) The remaining problems on this exam are based on the function .
(a) Derive the Maclaurin series for the function . Show
all of your work.
(b) Find the interval of convergence of the Maclaurin series from part
(a). Show all of your work.
Let's use the ratio test to check for absolute convergence.
(c) Use your answer to part (a) above to express ln(2) as an infinite
series.
ln(2) =
(d) Use your answer to part (a) above to find a power series representation
of the function .
=
(e) Write as
an infinite series. (You may just write out the first 5 or 6 terms.)