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Sullivan and Miranda - Calculus 1/e (Homework)

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 17 / 28

Due : Sunday, January 27, 2030 00:00 EST

Last Saved : n/a Saving...  ()

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Question
Points
1 2 3 4 5 6 7 8 9 10
–/12 –/1 –/1 –/3 –/0 –/3 –/1 –/1 –/2 –/3
Total
17/28 (60.7%)

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1. –/12 points SullivanCalc1 5.2.047. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6 7 8 9 10 11 12
–/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1
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–/12
 
For the function defined on the interval
[a, b],
 perform the following. (A computer algebra system is recommended.)
f(x) = 5 + 
x
 on
[1, 5]
(a) Complete the table of Riemann sums using a regular partition of
[a, b].
 (Round your answers to five decimal places.)
n 10 50 100
Using left endpoints
Using right endpoints
Using the midpoint

(b) Use a CAS to find the definite integral. (Round your answer to five decimal places.)
5
1
5 + 
x
 dx =


(c) Compare the answers in (a) and (b). Which Riemann sum gives the best approximation to the definite integral?
The Riemann sum using the with
n =
gave the best approximation.

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2. –/1 points SullivanCalc1 5.3.019-036d.XP.Tut. My Notes
Question Part
Points
Submissions Used
1
–/1
0/50
Total
–/1
 
Evaluate the definite integral using the Fundamental Theorem of Calculus.
 
π/4 (4 sin(x) + 2 cos(2x)) dx
0
 

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3. –/1 points SullivanCalc1 5.3.037. My Notes
Question Part
Points
Submissions Used
1
–/1
0/50
Total
–/1
 
Find
b
a
f(x) dx
 over the domain of f indicated in the graph.
WebAssign Plot

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4. –/3 points SullivanCalc1 5.3.077. My Notes
Question Part
Points
Submissions Used
1 2 3
–/1 –/1 –/1
0/50 0/50 0/50
Total
–/3
 
Let
f(x) = 
x
0
dt
4 − 4t2
,
0 < x < 1.
(a) Find
d
dx
 f(sin x).


(b) Is f one-to-one?
    

(c) Does f have an inverse?
    

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5. –/0 points SullivanCalc1 5.4.042. My Notes
Question Part
Points
Submissions Used
Total
–/0
 
The domain of the function f is a closed interval
[a, b].
 Find
b
a
f(x) dx.
f(x) = 
x2 if −3≤x ≤ −2
4 if −2 < x ≤ 4
x if 4 < x ≤ 9
9
−3
f(x) dx = (No Response)
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6. –/3 points SullivanCalc1 5.4.088. My Notes
Question Part
Points
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1 2 3
–/1 –/1 –/1
0/50 0/50 0/50
Total
–/3
 
Let A be the area in the first quadrant that is enclosed by the graphs of
y = 4x3, y = 
4
x
,
 the
x-axis,
 and the line
x = k,
 where
k > 1,
 as shown in the figure.
WebAssign Plot
(a) Find the area A as a function of k.
A =


(b) When the area is 9, what is k?
k =


(c) If the area A is increasing at the constant rate of 5 square units per second, at what rate is k increasing when
k = 16?
units per second

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7. –/1 points SullivanCalc1 5.5.008. My Notes
Question Part
Points
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1
–/1
0/50
Total
–/1
 
Find the indefinite integral. (Use C for the constant of integration.)
5
1 + x2
 dx

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8. –/1 points SullivanCalc1 5.5.059. My Notes
Question Part
Points
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1
–/1
0/50
Total
–/1
 
Oetzi the Iceman was found in 1991 by a German couple who were hiking in the Alps near the border of Austria and Italy. Carbon-14 testing determined that Oetzi died 5300 years ago. Assuming the half-life of carbon-14 is 5730 years, what percent of carbon-14 was left in his body? (An interesting note: In September 2010 the complete genome mapping of Oetzi was completed. Round your answer to two decimal places.)
%

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9. –/2 points SullivanCalc1 5.5.074. My Notes
Question Part
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1 2
–/1 –/1
0/50 0/50
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–/2
 
(a) Find
y'
 if
y = ln |csc x − cot x|.
y' =


(b) Use the result to show that
csc x dx = ln |csc x − cot x| + C.

This answer has not been graded yet.

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10. –/3 points SullivanCalc1 5.6.109. My Notes
Question Part
Points
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1 2 3
–/1 –/1 –/1
0/50 0/50 0/50
Total
–/3
 
Newton's Law of Cooling states that the rate of change of temperature with respect to time is proportional to the difference between the temperature of the object and the ambient temperature T. A thermometer that reads
6°C
 is brought into a room that is
35°C.
(a) Write the differential equation that models the temperature
u = u(t)
 of the thermometer at time t in minutes (min).
    

(b) Find the general solution of the differential equation.
    

(c) If the thermometer reads
12°C
 after 2 min, determine the temperature reading 5 min after the thermometer is first brought into the room. (Round your answer to two decimal places.)
°C

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