MAC2233
Chapter 5 Review
1. Evaluate 2
3
/
4
·
4

3
/
2
.
2. Simplify the expression
x

3
/
5
x
8
/
3
.
3. Solve the following equation for
x
: 5
x
2

3
=
1
5
2
x
.
4. Jada deposited an amount of money in a bank 5 years ago. If the bank
had been paying interest at the rate of 5%/year compounded daily (assuming
a 365 day year) and she has $15,000 on deposit today, what was her initial
deposit?
5. Determine the accumulated amount if $12,000 is invested for 5 years
at an interest rate of 4 %/year with continuous compounding.
6. Write the following expression as the logarithm of a single quantity:
ln 2 +
1
2
ln(
x
+ 1)

2 ln(1 +
√
x
)
.
7.
Use the laws of logarithms to expand and simplify the expression
ln (
e
x
1+
e
x
)
.
8. Use logarithms to solve the following equation for
t
:
A
1+
Be
t/
2
=
C.
9. How long will it take an investment of $6000 to grow to $7000 if the
investment earns interest at the rate of 6% compounded monthly?
10. Find the derivative of the function
f
(
x
) = (3
x
2

4)
e
x
.
11. Find the derivative of the function
g
(
t
) =
e

2
t
1+
t
2
.
12. Find the equation of the tangent line to the graph of
y
=
e

x
2
at the
point (1
,
1
/e
)
.
13. Find the absolute extrema of the function
h
(
x
) =
e
x
2

4
on [

2
,
2].
14. For the function
f
(
x
) =
e
x
+
e

x
2
find: intervals upon which the func
1
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tion is increasing and decreasing; intervals upon which the function is concave
upward and downward; local max and mins; inflection points; and vertical
and horizontal asymptotes. Sketch the curve.
15. Find the derivative of the function
f
(
x
) =
3 ln
x
x
2
.
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 Spring '08
 Smith
 Calculus, Exponential Function, Derivative, Logarithm, Convex function, Jada

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