Math 106 Sections C and D
Test 2 (50 points)
Name:
Show all your work to receive full credit for a problem.
There are six questions. Questions are printed on both sides of a page.
You may use any of the following facts:
Pn(x)=f(x0)+f0(x0)(x−x0)+f00(x0)
2! (x−x0)2+···+f(n)(x0)
n!(x−x0)n
|f(x)−Pn(x)|≤ Kn+1
(n+ 1)! |x−x0|n+1 Zudv =uv −Zvdu f(x)= 1
√2πs
exp −(x−m)2
2s2!
Z∞
1
1
xpdx converges for p>1 and diverges for p≤1. sin(2x)=2sinxcos x
Z1
0
1
xpdx converges for p<1 and diverges for p≥1. cos(2x)=cos
2x−sin2x
1. (7 points) Use comparisons to determine the convergence of the following integral.
Z∞
5
x2−1
√x+3x4+2x5dx .
