Deck 4: Section 5: Applications of Differentiation

Question 1

Sketch the graph of the function using any extrema, intercepts, symmetry, and asymptotes.

A)
B)
C)
D)
E)

Answer 1

Question 2

Find the limit.

A)
B) 2
C) 0
D)
E)

Answer 2

Question 3

Find the limit.

A)
B)
C) 1
D) 7
E)

Answer 3

Question 4

A container holds 3 liters of a 25% brine solution. A model for the concentration C of the mixture after adding x liters of a 0.67 % brine solution to the container and then draining x liters of the well-mixed solution is given as . Find . Round your answer to two decimal places.

A) 1.00 %
B) 0.17 %
C) 0.70 %
D) 0.67 %
E) 0.25 %

Question 5

Find the limit.

A)
B) 1
C) 0
D)
E)

Question 6

Find the limit.

A)
B)
C) 1
D) -6
E)

Question 7

The graph shows the temperature T, in degrees Fahrenheit, of molten glass t seconds after it is removed from a kiln. Find .

A)
B)
C)
D)
E)

Question 8

A heat probe is attached to the heat exchanger of a heating system. The temperature T (in degrees Celsius) is recorded t seconds after the furnace is started. A model for the data recorded for the first two minutes is given by . Find .

A)
B)
C)
D)
E)

Question 9

Sketch the graph of the relation using any extrema, intercepts, symmetry, and asymptotes.

A)
B)
C)
D)
E)

Question 10

For the function , use a graphing utility to complete the table and estimate the limit as x approaches infinity.

A) 0.8000
B) 1.8000
C) 1.2500
D) 2.2500
E) 0.2500

Question 11

Match the function with one of the following graphs.

A)
B)
C)
D)
E)

Question 12

Find the limit.

A)
B) 3
C)
D) -3
E) 5

Question 13

Sketch the graph of the relation using any extrema, intercepts, symmetry, and asymptotes.

A)
B)
C)
D)
E)

Question 14

Match the function with one of the following graphs.

A)
B)
C)
D)
E)

Question 15

A business has a cost of for producing x units. The average cost per unit is Find the limit of as x approaches infinity.

A) 333.3
B) 1
C) 500
D) 0
E) 1.5

Question 16

Match the function with one of the following graphs.

A)
B)
C)
D)
E)

Question 17

Find the limit.

A) 1
B) 0
C)
D)
E) does not exist

Question 18

For the function , use a graphing utility to complete the table and estimate the limit as x approaches infinity.

A) -0.2500
B) 1.0000
C) 2.1800
D) -0.9000
E) does not exist

Question 19

For the function , use a graphing utility to complete the table and estimate the limit as x approaches infinity.

A) -6
B) 2
C) 6
D) 0
E) None of the above

Question 20

Sketch the graph of the function using any extrema, intercepts, symmetry, and asymptotes.

A)
B)
C)
D)
E)

Question 21

Find the point on the graph of the function that is closest to the point . Round all numerical values in your answer to four decimal places.

A)
B)
C)
D)
E)

Question 22

Find the point on the graph of the function that is closest to the point .

A)
B)
C)
D)
E)

Question 23

A rectangular page is to contain square inches of print. The margins on each side are 1 inch. Find the dimensions of the page such that the least amount of paper is used.

A)
B)
C)
D)
E)