Final Test
Test Bank For For Applied Calculus for Business, Economics, and the Social and Life Sciences 11th Edition By Laurence Hoffmann, Gerald Bradley, David Sobecki, Michael Price With Midter & Final MC Answers Are at the end of Each Chapter
Chapter 1 1. Compute the indicated value of the given function. –2t 8 if t 1 ; f (–3) f (t ) 2 t 9 if t 1 A) 18 B) 0 C) 2 D) 14 2. Determine the domain of the given function. x2 1 f ( x) x3 A) all real numbers x except x = 1, x = –1, and x = –3 B) all real numbers x C) all real numbers x except x = –3 D) all real numbers x except x = 1 and x = 4 3. Find the difference quotient,
9 x f x h f x
f x h f x h
.
f x
A) B)
h f x h f x h
9 x x h
C)
9 xh
D)
f x h f x h f x h f x h
=9 =1
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Final Test
4. Find the indicated composite function. 1 f (x + 6) where f ( x) x 1 A) f (x + 6) = x 6 x 1 B) f (x + 6) = x6
C)
f (x + 6) = 1
D)
f (x + 6) =
3 x
1 6 x
5. Plot the given point in a rectangular coordinate system. (1, –5) A) C) y
y x
x (1, -5)
(1, -5)
(Each gridline represents one unit.)
(Each gridline represents one unit.)
B)
D) (1, -5) y
y (1, -5)
x
(Each gridline represents one unit.)
x
(Each gridline represents one unit.)
6. Find the distance between the given points. (–2, 6) and (3, 7) A) D = 6 B) D = 26 C) D 26 D) D 6
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Final Test
7. Sketch the graph of the given function. f ( x) x 2 2
(Tick marks are spaced one unit apart.)
8. Find the points of intersection (if any) of the given pair of curves. y x 2 and y = 3x – 2. A) There are no points of intersection. B) (2, 4) C) (1, 1), (2, 4) D) (0,0) 9. Find the slope (if possible) of the line that passes through the given pair of points. (28, 7) and (8, 3). 1 A) B) The slope is undefined. C) 5 D) 0 5 10. Find the slope and y-intercept (if they exist) of the line 8y = 7x. 7 and y-intercept is 0. A) Slope is 7 and y-intercept is 8. C) Slope is 8 8 and y-intercept is 0. B) Slope is D) Slope is 7 and y-intercept is 0. 7 11. Write an equation for the line through (5, 4) and parallel to the x-axis. A) y = 4 B) y = –4 C) x = –5 D) x = 5 12. The cost of renting a backhoe at one distributor is $325, plus $35 per day. Write a linear function C(x) that describes the cost of renting the backhoe for x days, then use your function to find how much it would cost to rent it for 12 days. A) C ( x) 35 x 313; $733 C) C ( x) 12 325 35 x ; $8,940 B)
C ( x) 325 x 35; $3,935
D)
C ( x) 325 35 x; $745
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Final Test
13. Each unit of a certain commodity costs p = 47x + 12 cents when x units of the commodity are produced. If all units are sold at this price, express the revenue derived from the sales as a function of x. A) 46x + 12 cents C) 48x + 12 cents B) 47 x 2 12 cents D) x(47x + 12) cents 14. A closed cylindrical can has a surface area of 120 square inches. Express the volume of the can as a function of its radius, r. A) V(r) = 60r cubic inches C) V (r ) π(60 r 3 ) cubic inches B) V (r ) 120 πr 2 cubic inches D) V (r ) πr (60 r 2 ) cubic inches 15. A closed box with a square base is to have a volume of 10 cubic meters. The material for the top and bottom of the box costs $5 per square meter, and the material for the sides costs $1 per square meter. Express the construction cost of the box as a function of the length of its base, x. 40 2 dollars A) C ( x) 10 x 2 C) C ( x) 2 x 2 10 dollars x x 10 dollars B) C ( x) x 2 40 x 2 dollars D) C ( x) 2 x 2 x 16. Two car rental agencies are competing. One agency rents cars for 50 dollars per day and 35 cents a mile; the other agency rents cars for 35 dollars per day and 45 cents a mile. For a 10 day trip, how many miles must you travel to have the total cost be the same with each agency? Round to the nearest whole mile , if necessary. A) 43 miles B) 1,500 miles C) 33 miles D) 150 miles 17. Find the indicated limit if it exists. lim x 4 x 3
A) 3
B) Does not exist
C) –1
D) 7
18. Find the indicated limit if it exists. x 2 3x 2 lim x 1 x2 1 3 A) Does not exist B) 6 C) D) 3 2 19. Find lim f x and lim f x . If the limiting value is infinite indicate whether it is + x
x
or –. f (x) = (5 – 9x)(x – 2) A) –– B) –0 C) ++ D) +0
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Final Test
20. Find lim f x and lim f x . If the limiting value is infinite indicate whether it is + x
x
or –. f x
4 2 x3 6 x3 – 6 x + 1
1 1 A) – B) –+ C) , 3 3
1 1 D) , 3 3
21. An efficiency consultant determines that when new workers are hired to wait tables at an upscale restaurant, the average number of tables they can wait on in a 6 hour shift is given by
5.3x 2 50 x 14 0.1x 0.8 where x is the number of shifts they've worked since being hired. What happens to an average waiter's productivity in the long run (as x )? A) It approaches 53 tables per shift. C) It approaches 23 tables per shift. B) It increases without bound. D) It approaches 14 tables per shift. N x
22. Find the indicated one-sided limit. If the limiting value is infinite, indicate whether it is + or –. x 2 lim x4 x4 1 1 A) B) C) 2 D) –2 4 4 23. Find the indicated one-sided limit. If the limiting value is infinite, indicate whether it is + or –. x 5 if x 2 lim f ( x) where f ( x) 2 x 2 x if x 2 A) There is none B) 7 C) 0 D) 4 24. List all values of x for which f (x) is not continuous. 2x 1 . f ( x) 2 x x 1 A) B) –1 C) None D) 0 and –1 2 25. List all the values of x for which the given function is not continuous. x3 if x 5 f ( x) 125 if x 5 A) x = 5 B) x = ±5 C) The function is continuous for all values of x.
D) x = 0
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