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Math 150 – FINAL EXAM – Spring 2006
[18] 1. Find the following limits. You must show all your work.
a) lim
x
→
3
x
2

8
x
+15
x
2
+
x

12
b) lim
x
→
0
tan3
x
x
c) lim
x
→∞
(
x

√
x
2

2
x
+5)
[10] 2. USING THE DEFINITION of derivative ±nd the derivative of
f
(
x
)=
√
x

2.
[30] 3. Find
f
±
(
x
) for the following functions. You do not need to simplify your answers.
a)
f
(
x
e
x

√
x
+ cot
x
b)
f
(
x
)=(
x
2
+5
x
+ 2)cosh
x
c)
f
(
x
1+ln
x
x
+ sin
x
d)
f
(
x
x
2
+4
x

1)
2
/
3
e)
f
(
x
x
sin
x
f)
f
(
x
±
x
1
dt
sin
2
t
+1
[8] 4. Let
y
(
x
) be de±ned implicitly by
x
3
+ln(
x
+
y
y
. Find
y
±
(
x
).
[12] 5. Determine an equation of the tangent line to the curve
f
(
x
) = ln(
x

1) at the point where the
graph crosses the
x
axis.
[10] 6. The combined electrical resistance
R
of
R
1
and
R
2
,
connected in parallel, is given by
1
R
=
1
R
1
+
1
R
2
where
R, R
1
and
R
2
are measured in ohms.
R
1
and
R
2
are increasing at rates of 1 and 1.5 ohms
per second, respectively. At what rate is
R
changing when
R
1
= 50 ohms and
R
2
= 75 ohms?
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This note was uploaded on 03/12/2012 for the course MATH 150 taught by Professor A during the Spring '05 term at University of Arizona Tucson.
 Spring '05
 A
 Math, Derivative, Limits

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