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E1-171S2002-copyright Joe Kahlig
Math 171
Exam I
Last Name(print):
February 14, 2002
First Name(print):
Signature:
Row:
You must show all appropriate work to receive full credit.
Work all problems on the paper provided. Turn in your exam with your work.
Do not work on the back on any page.
SCHOLASTIC DISHONESTY WILL NOT BE TOLERATED.
1. (6 points) Find a vector that is orthogonal to the vector < 4, 2 > and has a length of 3.
2. (6 points) A constant force F = 5i + 6j moves an object along the straight line from the point
(−1, 2) to the point (2, 3). Find the work done by F.
3. (6 points) Find the vector projection of < 5, 9 > onto j.
4. (5 points) Find the Cartesian equation of the parametric curve. x = 1 + cos(t) , y = 1 + sin2 (t).
5. (6 points) A particle is moving in the xy-plane and its position after t seconds is
r(t) = (t2 + t)i + (t − 4)j.
(a) Find the position of the particle at t = 2.
(b) Does the particle pass through the point (4, 8)? Justify your answer.
6. (10 points) Use the definition of the derivative to show that the derivative of f (x) =
f ′ (x) =
−2
(2x + 1)2
1
is
2x + 1
7. (10 points) For what value(s) of c and d that will the function f (x) be continuous. If there is
no value(s) that makes this true, then explain why.
f (x) =

 2x
for x < 1
+ d for 1 ≤ x ≤ 2

4x
for x > 2
cx2
8. (30 points) Find the exact values of the following limits:
(a) r(t) =
(b) lim
x→3+
*
t2 + t − 2 3
, t − 4t
t2 − t − 2
+
compute lim r(t)
t→1
x+1
− 3)
x2 (x
x2 − 2x − 8
x→4 x2 − 10x + 24
1
(d) lim cos(x) =
x→∞ x
p
(e) lim (x + x2 + 4x + 1) =
(c) lim
x→−∞
Continued on the back
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E1-171S2002-copyright Joe Kahlig
9. (21 points) Using the graph of f (x) below answer the following questions.
6
5
4
3
2
1
−7 −6 −5 −4 −3 −2 −1
−1
1
2
3
4
5
6
7
8
9
10
11
12
−2
−3
−4
(a) lim f (x) =
x→9
(b)
lim f (x) =
x→−3+
(c) lim− f (x) =
x→7
(d) For what values of x is the function not differentiable?
(e) For what values of x is the function not continuous?
(f) Approximate the value of f ′ (4). If not possible, explain why.