Calculus 1
Worksheet #100
Review with Calculator
** Remember- We must see any equations,integrals, and graphs, that you use to solve these problems**
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YOU MAY USE A CALCULATOR FOR PROBLEMS 1−15
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1. The figure above shows a 16–foot ladder leaning against a vertical wall. The tip of the ladder is sliding
down the wall at the rate of 5.6 feet per second. What is the rate of change, in radians per second, of the
angle θ at the instant when the tip of the ladder is 7 feet above the ground?
A) –6.223 B) –0.800 C) –0.389 D) –0.321 E) –0.070
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x

2. If F(x) =  tan t dt, then F ’ (0.5) = A) 0.089 B) 0.093 C) 0.546 D) 0.739 E) 1.139
0
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2
3. The average value of the function f ( x )  e  x on the closed interval [–1,1] is
a) 0.7 b) 0.75 c) 0.8
d)0.85 e) 0.9
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4. The slope of the line tangent to the graph of y = cos(2x) at x =
A)
–1.564
B) –0.782
C) –0.031
D) 0.657

7
E) 0.782
is
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5. The area of the region enclosed by the graphs of y = 7, x = 0, and y = 2x is closest to:
A) 9.0 B) 9.5 C) 10.0 D) 10.5 E) 11.0
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6.
The slope of the line tangent to the graph of y = e–x at x = 4 is
A) 0.050 B) 0.018 C) –0.007 D) –0.018 E) –0.050
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7.
A rectangle of length 2k is inscribed in the region between the x–axis and the graph of y = cos x, as
shown in the figure above. The value of k that maximizes the area of the rectangle is
A) 0.5000 B) 0.785 C) 0.860 D) 0.866 E) 6.280
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8. If f ( x ) is odd and f (a )  b , then f (  a )  ?
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9. The function f whose derivative is given by f ' (x) = 5x3 –15x + 7 has a local maximum at x =
A) – 1.930 B) –1.000 C) 0.511 D) 1.000 E) 1.419
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Revised: 3/17/2014
Calculus 1
Worksheet #100
Review with Calculator
** Remember- We must see any equations,integrals, and graphs, that you use to solve these problems**
______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
10. Car A is traveling south at 40 mph toward Millville, and Car B is traveling west at 30 mph toward Millville
at the same time. If both cars began traveling 100 miles outside of Millville at the same time, then at what
rate, in mph, is the distance between them decreasing after 90 minutes?
A) 35.00 B) 47.79 C) 50.00 D) 55.14 E) 68.01
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11. The graph of the function y = x5 – x2 + sin x changes concavity at x =
A) 0.324
B) 0.499
C) 0.506
D) 0.611
E) 0.704
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2
using Reimann sums with:
12. Approximate 
 x dx
0
(a) 4 left–endpoint rectangles,
(b) 4 right–endpoint rectangles,
(c) 4 midpoint rectangles,
(d) 4 trapezoids:
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2
13. 
 5x dx =
1
A) 2.726
B) 2.981
C) 3.354
D) 13.628
E) 20.442
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14. If ƒ(x) =
5
x3–2x , then ƒ ’ ( 3 ) = A) 0.129 B) 0.902 C) 0.906 D) 1.116 E) 2.173
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15. Given the function f(x) = ex/2 on the closed interval [–1,4], if c is the number guaranteed by the mean
value theorem, then c (correct to three decimal places) is
A) 0.998
B) 1.163
C) 1.996
D) 2.065
E) 2.325
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16. Free Response 2006B Problem #2. Do on a separate piece of paper. (ATTACHED BELOW)
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Answers:
1) C
10) B
2) D
11) B
3) B
12a) 1.5
4) A
12b) 2.5
5) E
12c) 2
6) D
12d) 2
7) C
13) A
8) –b
9) C
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Revised: 3/17/2014
Calculus 1
Worksheet #100
Review with Calculator
** Remember- We must see any equations,integrals, and graphs, that you use to solve these problems**
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AB/BC
2006
FORM B
#2
(CALCULATOR)
SCORE = ________
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Let f be the function defined for x  0 with f (0)  5 and f  , the
derivative of f, given by f   x   e
 x


 4 
sin  x 2  . The graph of
y  f   x  as shown at the right.
A Use the graph of f  to determine whether the graph of f is
concave up, concave down, or neither on the interval
1.7 < x <1.9. Explain your reasoning.
B On the interval 0  x  3 , find the value of x at which f has an
absolute maximum. Justify your answer
C Write an equation for the line tangent to the graph of f at x =2
Revised: 3/17/2014