 | Question 1: (4 points)
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Consider the function shown in the figure.
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(a)
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At what labeled points is the slope of the graph positive?
| (a) |
A
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| (b) |
B
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| (c) |
C
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| (d) |
D
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| (e) |
E
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| (f) |
F
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(b)
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At what labeled points is the slope of the graph negative?
| (a) |
A
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| (b) |
B
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| (c) |
C
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| (d) |
D
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| (e) |
E
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| (f) |
F
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(c)
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At which labeled point does the graph have the greatest (i.e., most positive) slope?
| (a) |
A
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| (b) |
B
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| (c) |
C
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| (d) |
D
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| (e) |
E
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| (f) |
F
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(d)
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At which labeled point does the graph have the least slope (i.e., negative and with the largest magnitude)?
| (a) |
A
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| (b) |
B
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| (c) |
C
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| (d) |
D
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| (e) |
E
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| (f) |
F
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| Question 2: (2 points)
Fill in the blanks:
Estimate the limit by substituting smaller and smaller values of
. Use radians. Give your answer to one decimal place.
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| Question 3: (2 points)
Fill in the blanks:
Use a graph to estimate the limit. Use radians.
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| Question 4: (1 point)
Fill in the blanks:
The population of the world reached 1 billion in
, 2 billion in
, 3 billion in
, 4 billion in
, 5 billion in
and 6 billion in
. Find the average rate of change of the population of the world, in people per minute, during each of these intervals.
____________
people/min from 1804 to 1927,
____________
people/min from 1927 to 1960,
____________
people/min from 1960 to 1974,
____________
people/min from 1974 to 1987,
____________
people/min from 1987 to 1999.
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| Question 5: (6 points)
Fill in the blanks:
The graph of
in the figure gives the position of a particle at time
.
Number the following quantities 1 through 6, smallest to largest.
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____
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(A) average velocity between
and
, |
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(B) average velocity between
and
, |
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(C) instantaneous velocity at
, |
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(D) instantaneous velocity at
, |
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(E) instantaneous velocity at
, |
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(F) instantaneous velocity at
. |
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| Question 6: (4 points)
Fill in the blanks:
Using the figures, estimate
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| Question 7: (2 points)
Fill in the blanks:
Use algebra to evaluate the limit.
____
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| Question 8: (2 points)
Fill in the blanks:
Use algebra to evaluate the limit. [Hint: Multiply by
in numerator and denominator.]
____
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| Question 9: (3 points)
Fill in the blanks:
Use algebra to evaluate the limits, if they exist. If the limit does not exist, write “none”.
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| Question 10: (3 points)
Fill in the blanks:
Use algebra to evaluate the limits, if they exist. If the limit does not exist, write “none”.
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| Question 11: (2 points)
Assuming that limits as
have the properties listed for limits as
, use algebraic manipulations to evaluate
for the function
Write “inf” for
.
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| Question 12: (2 points)
Assuming that limits as
have the properties listed for limits as
, use algebraic manipulations to evaluate
for the function
Write “inf” for
.
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| Question 13: (2 points)
Find the derivative of
at
algebraically.
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| Question 14: (2 points)
Find the derivative of
at
algebraically.
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| Question 15: (2 points)
Find the derivative of
at
algebraically.
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