Deck 2: Section 1: Limits and Their Properties

Question 1

Decide whether the following problem can be solved using precalculus, or whether calculus is required. If the problem can be solved using precalculus, solve it. If the problem seems to require calculus, use a graphical or numerical approach to estimate the solution. Find the distance traveled in 16 seconds by an object traveling at a constant velocity of 20 feet per second.

A) calculus, 320 ft
B) calculus, 340 ft
C) precalculus, 320 ft
D) calculus, 640 ft
E) precalculus, 640 ft

Answer 1

precalculus, 320 ft

Question 2

Decide whether the following problem can be solved using precalculus, or whether calculus is required. If the problem can be solved using precalculus, solve it. If the problem seems to require calculus, use a graphical or numerical approach to estimate the solution. A cyclist is riding on a path whose elevation is modeled by the function where x and are measured in miles. Find the rate of change of elevation when x = 5.

A) calculus, 2
B) precalculus, 0.2
C) calculus, 0.2
D) precalculus, 2
E) precalculus, 0.45

Answer 2

precalculus, 0.2

Question 3

Use the rectangles in the following graph to approximate the area of the region bounded by .

A) 3.9082
B) 2.6055
C) 1.9541
D) 1.4656
E) 0.9770

Answer 3

1.9541

Question 4

Decide whether the following problem can be solved using precalculus, or whether calculus is required. If the problem can be solved using precalculus, solve it. If the problem seems to require calculus, use a graphical or numerical approach to estimate the solution. Find the distance traveled in 20 seconds by an object moving with a velocity of feet per second.

A) calculus, 162.4485 ft
B) precalculus, 163.7985 ft
C) calculus, 165.4777 ft
D) precalculus, 165.4777 ft
E) precalculus, 162.4485 ft

Question 5

Use the rectangles in the graph given below to approximate the area of the region bounded by Round your answer to three decimal places.

A) 2.481 units²
B) 6.371 units²
C) 3.585 units²
D) 6.872 units²
E) 6.903 units²

Question 6

Decide whether the following problem can be solved using precalculus, or whether calculus is required. If the problem can be solved using precalculus, solve it. If the problem seems to require calculus, use a graphical or numerical approach to estimate the solution. Find the area of the shaded region bounded by the triangle with vertices (0,0), (8,9), (17,0).

A) precalculus , 153
B) calculus , 229.5
C) precalculus , 76.5
D) precalculus , 229.5
E) calculus , 153

Question 7

Consider the length of the graph of Approximate the length of the curve by finding the sum of the lengths of four line segments, as shown in following figure. Round your answer to two decimal places.

A) 6.11
B) 8.12
C) 5.66
D) 8.49
E) 7.11

Question 8

Decide whether the following problem can be solved using precalculus, or whether calculus is required. If the problem can be solved using precalculus, solve it. If the problem seems to require calculus, use a graphical or numerical approach to estimate the solution. Find the area of the shaded region.

A) calculus , 11
B) precalculus , 11
C) precalculus , 13
D) calculus , 16
E) precalculus , 16

Question 9

Use the rectangles in the following graph to approximate the area of the region bounded by .

A) 0.7850
B) 1.5700
C) 3.1400
D) 1.1775
E) 1.0519

Question 10

Decide whether the following problem can be solved using precalculus, or whether calculus is required. If the problem can be solved using precalculus, solve it. If the problem seems to require calculus, use a graphical or numerical approach to estimate the solution. A cyclist is riding on a path whose elevation is modeled by the function where x and are measured in miles. Find the rate of change of elevation when x = 4.

A) precalculus, 0.08
B) calculus, 0.2
C) calculus, 0.64
D) calculus, 0.08
E) precalculus, 0.2