1.1 A Preview of Calculus 43
1.1 A Preview of Calculus
Multiple Choice
Identify the choice that best completes the statement or answers the 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
____ 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.
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
____ 3. 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.
44 Chapter 1: Limits and Their Properties
a. precalculus, 0.08
b. calculus, 0.2
c. calculus, 0.64
d. calculus, 0.08
e. precalculus, 0.2
____ 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.
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
1.1 A Preview of Calculus 45
____ 5. 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
____ 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.
a. calculus , 11
b. precalculus , 11
c. precalculus , 13
46 Chapter 1: Limits and Their Properties
d. calculus , 16
e. precalculus , 16
____ 7. Consider the function and the point on the graph of f. Graph f
and the secant line passing through and for .
a. d.
b. e.
c.
1.1 A Preview of Calculus 47
____ 8. Consider the function and the point on the graph of f. Find the
slope of the secant line passing through and for . Round your answer to
four decimal places.
a. m=0.1000
b. m=0.0122
c. m=0.0122
d. m=0.3133
e. m=0.1000
____ 9. Consider the function and the point P(64,8) on the graph of f.
Consider the secant lines passing through P(64,8) and Q(x, f(x)) for x values of 61, 63, and 65. Find
the slope of each secant line to four decimal places.
(Think about how you could use your results to estimate the slope of the tangent line of f at P(64,8),
and how to improve your approximation of the slope.)
a. 0.0633 , –0.0627 , 0.0623
b. 0.0633 , 0.0627 , 0.0623
c. 0.0317 , 0.0314 , 0.0312
d. 0.0633 , –0.0627 , –0.0623
e. –0.0317 , –0.0314 , –0.0312
____ 10. Consider the function and the point on the graph of f. Estimate
the slope m of the tangent line of f at . Round your answer to four decimal places.
a. m=0.1667
b. m=0.0832
c. m=0.3800
d. m=0.0556
e. m=0.0833
48 Chapter 1: Limits and Their Properties
____ 11. Consider the function and the point on the graph of f. Graph f
and the secant line passing through and for .
a. d.
b. e.
c.
1.1 A Preview of Calculus 49
____ 12. Consider the function and the point on the graph of f. Find
the slope of the secant line passing through and for . Round your answer
to one decimal place.
a. 3.5
b. 2.0
c. 3.0
d. 4.5
e. 9.0
____ 13. Consider the function and the point on the graph of f.
Estimate the slope of the tangent line of f at .
a. 10
b. 3
c. 8
d. 2
e. 9
____ 14. 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
50 Chapter 1: Limits and Their Properties
____ 15. 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
1.1 A Preview of Calculus 51
1.1 A Preview of Calculus
Answer Section
MULTIPLE CHOICE