Larson_Calculus_10e ch05sec01
MULTIPLE CHOICE
1. What is the domain of the function ?
a.
b.
c.
d.
e.
2. What is the domain of the function ?
a.
b.
c.
d.
e.
3. Write the following expression as a logarithm of a single quantity.
a.
b.
c.
d.
e.
4. Write the following expression as a logarithm of a single quantity.
a.
b.
c.
d.
e.
5. Find the following limit if it exists: . Use when appropriate.
a.
b.
c.
d.
e.
6. Find the following limit if it exists: . Use when appropriate.
a.
b.
c.
d.
e.
7. Find an equation of the tangent line to the graph of at the point (1,0).
a.
b.
c.
d.
e.
8. Differentiate the function .
a.
b.
c.
d.
e.
9. Differentiate the function .
a.
b.
c.
d.
e.
10. Find the derivative of the function .
a.
b.
c.
d.
e.
11. Find the derivative of the function .
a.
b.
c.
d.
e.
12. Find the derivative of the function .
a.
b.
c.
d.
e.
13. Find the derivative of the function .
a.
b.
c.
d.
e.
14. Find the slope-intercept equation of the line tangent to the graph of when .
a.
b.
c.
d.
e.
15. Use implicit differentiation to find .
a.
b.
c.
d.
e.
16. Use implicit differentiation to find .
a.
b.
c.
d.
e.
17. Use implicit differentiation to find at the point .
a.
b.
c.
d.
e.
18. Locate any relative extrema and inflection points of the function . Use a graphing utility
to confirm your results.
a.
relative minimum value: ; no inflection points
b.
relative minimum value: inflection point:
c.
relative maximum value: inflection point:
d.
relative minimum value: no inflection points
e.
relative maximum value: ; no inflection points
19. Determine the x-coordinate(s) of any relative extrema and inflection points of the function .
a.
relative minimum: ; no inflection points
b.
relative maximum: ; inflection point:
c.
no relative maximum or minimum; inflection point:
d.
no relative extrema or inflection points.
e.
relative minimum: ; inflection point:
20. Determine the x-coordinate(s) of any relative extrema and inflection points of the function .
a.
relative minimum: ; inflection point:
b.
no relative extrema; inflection point:
c.
relative minimum: ; no inflection points
d.
no relative extrema; inflection point:
e.
relative maximum: inflection point:
21. Use logarithmic differentiation to find the derivative of .
a.
b.
c.
d.
e.
22. Suppose the term of a mortgage t (in years) can be approximated by
where x is the monthly payment in dollars. Use the model to approximate the term of a home mortgage
for which the monthly payment is $ . What is the total amount paid? Round your answer to the
nearest cent. Your answer may be slightly different depending on the number of digits your technology
uses in computations.
a.
$
b.
$
c.
$
d.
$
e.
$
23. Suppose the term of a mortgage t (in years) can be approximated by
where x is the monthly payment in dollars. Find the instantaneous rate of change of t with respect to x
when . Round your answer to four decimal places.
a.
0.0044
b.
–0.1619
c.
0.0619
d.
–0.0619
e.
–0.0044
24. The relationship between the number of decibels and the intensity I of sound in watts per centimeter
squared is . Determine the number of decibels of a sound with an intensity of
watts per square centimeter.
a.
250 decibels
b.
65 decibels
c.
70 decibels
d.
decibels
e.
75 decibels
25. Suppose the table below shows the temperature at which a given liquid boils at selected
pressures p (pounds per square inch). A model that approximates the data is
. Find the rate of change of T with respect to p when P = 20. Round
your answer to two decimal places.
P
5
10
14.696
(1 atm)
20
30
40
60
80
100
T
234.68
288.88
320.55
346.89
383.19
410.28
450.7
481.26
506.22
a.
b.
c.
d.
e.
26. Suppose the table below shows the temperature at which a given liquid boils at selected
pressures p (pounds per square inch). A model that approximates the data is
. Use a graphing utility to graph .
P
5
10
14.696(1 atm)
20
30
40
60
80
100
T
234.68
288.88
320.55
346.89
383.19
410.28
450.7
481.26
506.22
a.
d.
b.
e.
c.
27. Suppose the table below shows the temperature at which a given liquid boils at selected
pressures p (pounds per square inch). A model that approximates the data is
. Find .
P
5
10
14.696
(1 atm)
20
30
40
60
80
100
T
204.16
236.64
256.08
272.55
295.68
313.29
340.12
360.86
378.07
a.
1
b.
0
c.
d.
e.