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Name
17 September 2009
Teaching Assistant
Hour Test 1
Math 1501 J Andrew
Instructions:
1.
Closed book.
2.
Show your work and explain your answers and reasoning.
3.
Calculators may be used, but are by no means necessary.
Pay particular
attention to instruction 2.
To receive credit, you must show your
work.
Unexplained answers, and answers not supported by the work
you show, will not receive credit.
4.
Express your answers in simplified form.
1.
(25)
Either evaluate the given limit or explain why it does not exist.
Don't even think
about using L'Hospital's rule.
a.
6
5
2
3
lim
2
2
2
+

+

→
x
x
x
x
x
b.
6
5
1
2
lim
2
2
2
+

+

→
x
x
x
x
x
c.
)
3
sin(
lim
0
x
x
x
→
d.
2
1
)
sin(
lim
2
π


→
x
x
x
2.
(25)
a.
Use the definition of the derivative to compute
)
0
(
'
f
for
x
x
x
f
=
)
(
.
b.
Calculate the derivative of
i.
)
2
sin(
)
sin(
)
(
x
x
x
x
f
=
ii.
1
1
)
(
2
2
+

=
x
x
x
g
iii.
)
(
cos
)
(
2
3
x
x
h
=
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Page 2 of 3
Hour Test 1
Teaching Assistant
17 September 2009
3.
(25)
a.
Find the equation of the line tangent to the graph of
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 Fall '08
 N/A
 Math

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