Name
Student ID #
Math 1320
Spring 2014
SAMPLE EXAM II
This is only to give you a general idea of what to expect. The actual exam
may or may not include problems similar to those given here, and it may be
longer or shorter.
Instructions: Show all of your work for full credit.
Problem
1.
2.
3.
4.
5.
Points
20
20
20
20
20
TOTAL
Score
(20 points) 1. Beginning with the geometric series, derive a power series representa2x
tion for f (x) =
, and find the radius of convergence.
4 + x2
(20 points) 2. Find the Taylor series expansion centered at a = 1 for f (x) = x3 − x2 .
1
(20 points) 3. (a) Find the vector projection of b = h1, 4, −3i onto a = h−2, 1, 5i.
(b) What is the cosine of the angle between a and b?
(20 points) 4. Find the volume of the parallelepiped with edges determined by the
vectors a = h1, 2, 3i, b = h1, 0, −1i, and c = h0, −2, 1i.
2
(20 points) 5. Find parametric equations describing the tangent line to the curve parameterized by r(t) = ht2 + 1, cos t, 2et i, at the point (1, 1, 2).
3