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Math 20B
First Exam
4:40 PM
January 29, 2001
•
Please put your name, ID number, and section number (or time) on your blue book.
•
The exam is CLOSED BOOK.
•
Calculators are NOT allowed.
•
You must show your work to receive credit.
1. (48 pts.) Evaluate the following. Remember to show your work!
(a) lim
x
→
0
cos
x

1
e
x

1
.
(b)
F
0
(
x
)
given that
F
(
x
)=
Z
2
√
x
cos(
t
2
)
dt.
(c)
Z
e
t
√
1+
e
t
dt.
(d)
Z
2
0

x

1

dx.
2. (20 pts.) (a) Verify that ln

sin
u

is an antiderivative of cot
u
.
(b) Compute
Z
π/
2
π/
4
cot
xdx
.
Your ﬁnal answer may contain logarithms,
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Unformatted text preview: but it should NOT contain trig functions. 3. (12 pts.) Verify the inequality Z 1 p 2 + x 2 dx 3 without evaluating the integral. 4. (a) (15 pts.) Given the table of information below, use a linear approximation to estimate g (16). x 5 10 15 g ( x ) 0 20 35 45 (b) (5 pts.) Do you think your prediction is an overestimate or underestimate? Why? You must give a reason to receive credit. END OF EXAM...
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This note was uploaded on 06/17/2009 for the course MATH 20B taught by Professor Justin during the Winter '08 term at UCSD.
 Winter '08
 Justin
 Math, Calculus

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