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Math 21H
Jan. 29, 1998
Test #1
Name:
Read each question carefully, and be sure to show clearly how you got your answers as well as
what your answers are.
1. Diﬀerentiate the following functions:
(a) [9 points]
f
(
x
)=
e
√
x
(b) [9 points]
f
(
x
) = arcsin(
e
x
)
(c) [9 points]
f
(
x
x

x
2. Find these integrals:
(a) [9 points]
Z
e
x
e
x
+1
dx
(b) [9 points]
Z
1
x
2
+4
dx
3. [9 points] Solve for
x
:l
n
x
+ ln(
x

1)=ln2+ln6
4. Find the following limits:
(a) [9 points] lim
x
→
0
x
+ sin 3
x
x

sin 3
x
(b) [9 points] lim
x
→
0
+
ln
x
√
x
(c) [9 points] lim
x
→∞
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