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Math 11B
Final Review Problems
Note: these problems represent some of the topics that were covered since Midterm 2. Bear in mind that the
final will be comprehensive, with a slight emphasis on the most recent topics. See earlier review problems
and solutions to Midterms 1 and 2 for review of earlier topics.
1. Use Integration by parts to prove the following formula: ∫∫ −−= dxexanexadxex axnaxnaxn 11 .
2. Find the linear approximation to xexf =)( for x near 2.
3. Find the thn degree Taylor polynomial of the following functions )(xf for x near a.
a. xexf =)( , 5=n , 0=a
b. xexf =)( , 5=n , 1=a
c. 2)( xexf −= , 10=n , 0=a (Hint: substitute into your answer to part a) Note: in an earlier version of
this document, the hint said part b, which was an error. Let me expand on the hint a little. Take your
answer for part a (not b), and replace x everywhere you see it by 2x− . This is much easier than
taking 10 derivatives of 2xe− .
d. xxf sin)( = , 7=n , 0=a
e. xxf += 1)( ,...

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