i need someone to answer all these questions in the word file please show solving step by step till you reach the final result. look at the file down you will find all questions
exam__1___spring_2019.pdf
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3/2/2019
Exam #1 – Spring 2019
WebAssign
Exam #1 – Spring 2019 (Exam)
Current Score : 49.22 / 70
Khaled Aldossari
MATH 152, section 03, Spring 2019
Instructor: Shurron Farmer
Due : Wednesday, March 6, 2019 10:30 PM ESTLast Saved : n/a Saving… ()
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1. 0.96/1.89 points | Previous AnswersLarCalcET6 4.7.023.MI.
A right triangle is formed in the first quadrant by the x- and y-axes and a line through the point (1, 2) (see figure below).
(a) Write the length L of the hypotenuse as a function of x.
L=
√x2+4×2(x−1)2
,x>1
(b) Use a graphing utility to approximate x graphically such that the length of the hypotenuse is a minimum.
Find the value of x that produces the minimum value L. (Round your answer to three decimal places.)
x = 2.587
(c) Find the vertices of the triangle such that its area is a minimum. (Order your answers from smallest to largest x, then from
smallest to largest y.)
(x, y) = (
)
(x, y) = (
)
(x, y) = (
)
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2. 1.89/1.89 points | Previous AnswersLarCalcET6 4.7.026.
A rectangle is bounded by the x-axis and the semicircle in the positive y-region (see figure). Find the dimensions of the largest rectangle
that can be inscribed in a semicircle of radius r.
r√2
(smaller value)
√2 r
(larger value)
3. 1.89/1.89 points | Previous AnswersLarCalcET6 4.7.030.
A cylindrical package to be sent by a postal service can have a maximum combined length and girth (perimeter of a cross section) of
114 inches. Find the dimensions of the package of maximum volume that can be sent. (The cross section is circular.)
38π
radius
in
38
length
in
4. 1.89/1.89 points | Previous AnswersLarCalcET6 5.1.014.
Find the indefinite integral and check your result by differentiation. (Use C for the constant of integration.)
x +
1
9
x
dx
2x√x3+2√x9+C
5. 1.89/1.89 points | Previous AnswersLarCalcET6 5.1.030.
Find the indefinite integral and check the result by differentiation. (Use C for the constant of integration.)
(cos x + 4x) dx
$$sin(x)+4xln(4)+C
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6. 1.89/1.89 points | Previous AnswersLarCalcET6 5.1.040.
Find the particular solution that satisfies the differential equation and the initial condition.
f ”(x) = sin(x),
f ‘(0) = 7,
f(0) = 6
f(x) =
−sin(x)+8x+6
7. 1.89/1.89 points | Previous AnswersLarCalcET6 5.1.055.
Use a(t) = -32 ft/sec2 as the acceleration due to gravity. (Neglect air resistance.)
A balloon, rising vertically with a velocity of 16 feet per second, releases a sandbag at the instant when the balloon is 80 feet above the
ground.
(a) How many seconds after its release will the bag strike the ground? (Round your answer to two decimal places.)
t = 2.79
sec
(b) At what velocity will it strike the ground? (Round your answer to three decimal places.)
v = -73.321
ft/sec
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8. –/1.89 pointsLarCalcET6 5.1.066.MI.
A car traveling at 45 miles per hour is brought to a stop, at constant deceleration, 132 feet from where the brakes are applied. (Round
your answers to two decimal places.)
(a) How far has the car moved when its speed has been reduced to 30 miles per hour?
ft
(b) How far has the car moved when its speed has been reduced to 15 miles per hour?
ft
(c) Draw the real number line from 0 to 132, and plot the points found in parts (a) and (b).
What can you conclude?
Each time, less time is needed to reach the next speed reduction.
Each time, more distance is needed to reach the next speed reduction.
Each time, more time is needed to reach the next speed reduction.
Each time, less distance is needed to reach the next speed reduction.
Each time, the distance and time needed to reach the next speed reduction does not change.
9. 1.89/1.89 points | Previous AnswersLarCalcET6 5.1.071.
Find a function f such that the graph of f has a horizontal tangent at (1, 0) and f ”(x) = 8x.
f(x) =
4×33−4x+83
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10.–/1.89 pointsLarCalcET6 5.2.011.
Use sigma notation to write the sum.
4
5
n
−
5
n
5
n
+…+
5n
n
4
−
5n
n
5
n
i=1
11.–/1.89 pointsLarCalcET6 5.2.022.
Use the summation formulas to rewrite the expression without the summation notation.
n
S(n) =
3j + 4
n2
j=1
Use the result to find the sums for n = 10, 100, 1000, and 10,000.
n = 10
n = 100
n = 1000
n = 10,000
12.–/1.89 pointsLarCalcET6 5.2.035.
Use upper and lower sums to approximate the area of the region using the given number of subintervals (of equal width). (Round your
answers to three decimal places.)
y=
7
x
upper sum
lower sum
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13.–/1.89 pointsLarCalcET6 5.2.051.
Use the limit process to find the area of the region between the graph of the function and the x-axis over the given interval.
y = 64 − x3, [2, 4]
Sketch the region.
14.1.89/1.89 points | Previous AnswersLarCalcET6 5.3.008.
Evaluate the definite integral by the limit definition.
1
−2
(2×2 + 3) dx
15
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15.–/1.89 pointsLarCalcET6 5.3.046.MI.
3
Given
6
f(x) dx = 8 and
0
f(x) dx = −5 , evaluate the following.
3
6
(a)
f(x) dx
0
3
(b)
f(x) dx
6
3
(c)
f(x) dx
3
6
(d)
3
−5f(x) dx
16.1.89/1.89 points | Previous AnswersLarCalcET6 5.4.026.
Evaluate the definite integral. Use a graphing utility to verify your result.
7
x2 − 6x + 5 dx
0
71/3
17.–/1.89 pointsLarCalcET6 5.4.053.
Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the given interval. (Enter your answers
as a comma-separated list.)
f(x) = 2 sec2 x, [−π/4, π/4]
c=
18.0.94/1.89 points | Previous AnswersLarCalcET6 5.4.059.
Find the average value of the function over the given interval. (Round your answer to three decimal places.)
f(x) = −sin x,
[0, π]
-0.637
Find all values of x in the interval for which the function equals its average value. (Enter your answers as a comma-separated list. Round
your answers to three decimal places.)
x=
$$2.451,3.833
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19.–/1.89 pointsLarCalcET6 5.4.066.
The velocity v of the flow of blood at a distance r from the central axis of an artery of radius R is given below, where k is the constant
proportionality.
v = k(R2 − r2)
Find the average rate of flow of blood along a radius of the artery. (Use 0 and R as the limits of integration.)
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20.–/1.89 pointsLarCalcET6 5.4.077.
Let
x
g(x) =
0
f(t) dt
where f is the function whose graph is shown in the figure.
(a) Estimate g(0), g(2), g(4), g(6), and g(8).
g(0) =
g(2) =
g(4) =
g(6) =
g(8) =
(b) Find the largest open interval on which g is increasing. (Enter your answer using interval notation.)
Find the largest open interval on which g is decreasing. (Enter your answer using interval notation.)
(c) Identify any extrema of g.
g has a —Select—
of
at x =
.
(d) Sketch a rough graph of g.
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21.1.89/1.89 points | Previous AnswersLarCalcET6 5.4.089.MI.
Use the Second Fundamental Theorem of Calculus to find F ‘(x).
F(x) =
F ‘(x) =
x
−5
t 4 + 9 dt
√x4+9
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22.1.89/1.89 points | Previous AnswersLarCalcET6 5.4.098.
Find F ‘(x).
x5
F(x) =
0
F ‘(x) =
sin θ5 dθ
5x4sin(x25)
23.1.89/1.89 points | Previous AnswersLarCalcET6 5.5.059.
Find an equation for the function f that has the given derivative and whose graph passes through the given point.
Derivative
Point
f ‘(x) = 2x(4×2 − 10)2
(2, 10)
f(x) =
(4×2−10)312−8
24.1.89/1.89 points | Previous AnswersLarCalcET6 5.5.076.
Evaluate the definite integral. Use a graphing utility to verify your result.
7
x
8x − 7
1
dx
398
25.1.89/1.89 points | Previous AnswersLarCalcET6 5.5.079.
Evaluate the definite integral. Use a graphing utility to verify your result.
4
1
e4/x
x2
dx
e4−e4
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26.–/1.89 pointsLarCalcET6 5.5.105.
Consider the following function.
f(x) = kxn(1 − x)m,
0≤x≤1
The function shown above, where n > 0, m > 0, and k is a constant, can be used to represent various probability distributions.
1
0
f(x) dx = 1
If k is chosen such that the integral of f(x) (shown above) is 1, the probability that x will fall between a and b (0 ≤ a ≤ b ≤ 1) is as
follows.
b
Pa, b =
f(x) dx
a
The probability that a person will remember between 100a% and 100b% of material learned in an experiment is given below, where x
represents the proportion remembered. (See figure.)
b
Pa, b =
a
15
x
4
1 − x dx
(a) For a randomly chosen individual, what is the probability that he or she will recall between 50% and 75% of the material?
(Round your answer to one decimal place.)
%
(b) What is the median percent recall? That is, for what value of b is it true that the probability of recalling 0 to b is 0.5? (Round
your answer to one decimal place.)
%
27.1.89/1.89 points | Previous AnswersLarCalcET6 5.7.019.
Find the indefinite integral. (Use C for the constant of integration.)
x4 + x − 49
x2 + 7
dx
$$ln(|x2+7|)2+x3−21×3+C
28.1.89/1.89 points | Previous AnswersLarCalcET6 5.7.027.MI.
Find the indefinite integral by u-substitution. (Hint: Let u be the denominator of the integrand. Remember to use absolute values where
appropriate. Use C for the constant of integration.)
1
9+
2x
dx
$$√2x−9ln(|√2x+9|)+C
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29.1.89/1.89 points | Previous AnswersLarCalcET6 5.7.087.
Find a value of x such that the following relation holds true.
x
1
x
3
1
dt =
dt
t
1/100 t
x = 10
30.1.89/1.89 points | Previous AnswersLarCalcET6 5.8.010.
Find the indefinite integral. (Use C for the constant of integration.)
5
x
25 − (ln x)2
dx
5arcsin(ln(x)5)+C
31.1.89/1.89 points | Previous AnswersLarCalcET6 5.8.020.
Find the indefinite integral. (Use C for the constant of integration.)
x−4
(x + 2)2 + 16
dx
$$ln((x+2)2+16)−3arctan(x+24)2+C
32.1.89/1.89 points | Previous AnswersLarCalcET6 5.8.036.
Find or evaluate the integral by completing the square. (Remember to use absolute values where appropriate. Use C for the constant of
integration.)
8x − 7
x2 + 2x + 2
dx
4ln(|x2+2x+2|)−15arctan(2x+22)+C
33.1.89/1.89 points | Previous AnswersLarCalcET6 5.8.046.
Use the specified substitution to find or evaluate the integral.
dx
1
0
2
3−x
x+1
,
u=
x+1
π12
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34.1.89/1.89 points | Previous AnswersLarCalcET6 5.9.030.
Find the derivative of the function.
y = 2x cosh(x) − 2 sinh(x)
y’ =
2xsinh(x)
35.1.89/1.89 points | Previous AnswersLarCalcET6 5.9.055.
Evaluate the integral.
ln 2
0
tanh x dx
ln(54)
36.1.89/1.89 points | Previous AnswersLarCalcET6 5.9.065.
Find the derivative of the function.
y = cosh−1(9x)
y’ =
9√81×2−1
37.1.96/1.96 points | Previous AnswersLarCalcET6 5.9.078.
Find the integral using the formulas from Theorem 5.20. (Remember to use absolute values where appropriate. Use C for the constant of
integration.)
x
dx
4 − x4
ln(|x2+2|)−ln(|x2−2|)8+C
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