Name:
Math 106C: Fall 2012
Exam 2: November 2
Write all your answers in your exam book. Label problems clearly and circle final answers. Put your name
on your exam and turn it in with your exam book.
Correct answers accompanied by incorrect or incomplete work will not receive full credit. Good Luck!
๎
sin2x=1
2โcos(2x)
2๎
cos2x=1
2+cos(2x)
2๎
sin(2x) = 2 sin xcos x
๎
Zsec2x dx = tan x+C๎
Zsec xtan x dx = sec x+C
๎
Zsec x dx = ln |sec x+ tan x|+C๎
Ztan x dx = ln |sec x|+C
๎
Zsecnx dx =secnโ2xtan x
nโ1+nโ2
nโ1Zsecnโ2x dx (n > 1)
๎
d
dxbx= (ln b)bx๎
d
dx tan x= sec2x๎
d
dx sec x= sec xtan x
1. (10 points) Evaluate the integral Z(11zโ4) sin(3z)dz.
2. (10 points each) Evaluate the following definite integrals. If an integral is improper and diverges, state
that.
(a) Z2
1
5x+ 2
(x+ 1)(2xโ1) dx
(b) Z5
0
ex
exโ1dx
(c) Z2
โ1
1
3
โxdx
3. (15 points)
(a) Find P3(x)the third order Taylor Polynomial of f(x) = 3
โxbased at x0= 8.
(b) Use your answer in (a) to estimate 3
โ9to 5 decimal places.
