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Single Variable Calculus: Early Transcendentals, Volume I
8th Edition
ISBN: 9781305270343
Author: James Stewart
Publisher: Cengage Learning
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Chapter 5.4, Problem 22E
To determine
To calculate: The value of the
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Good Day,
Would appreciate any assistance with this query.
Regards,
This question builds on an earlier problem. The randomized numbers may have changed, but have your work for the previous problem available to help with this one.
A 4-centimeter rod is attached at one end to a point A rotating counterclockwise on a wheel of radius 2 cm. The other end B is free to move back and forth along a horizontal bar that goes through the center of the wheel. At time t=0 the rod is situated as in the diagram at the left below. The
wheel rotates counterclockwise at 1.5 rev/sec. At some point, the rod will be tangent to the circle as shown in the third picture.
A
B
A
B
at some instant, the piston will be tangent to the circle
(a) Express the x and y coordinates of point A as functions of t:
x= 2 cos(3πt)
and y= 2 sin(3t)
(b) Write a formula for the slope of the tangent line to the circle at the point A at time t seconds:
-cot(3πt)
sin(3лt)
(c) Express the x-coordinate of the right end of the rod at point B as a function of t: 2 cos(3πt) +411-
4
-2 sin (3лt)
(d)…
5. [-/1 Points]
DETAILS
MY NOTES
SESSCALCET2 6.5.AE.003.
y
y= ex²
0
Video Example
x
EXAMPLE 3
(a) Use the Midpoint Rule with n = 10 to approximate the integral
कर
L'ex²
dx.
(b) Give an upper bound for the error involved in this approximation.
SOLUTION
8+2
1
L'ex² d
(a) Since a = 0, b = 1, and n = 10, the Midpoint Rule gives the following. (Round your answer to six decimal places.)
dx Ax[f(0.05) + f(0.15) + ... + f(0.85) + f(0.95)]
0.1 [0.0025 +0.0225
+
+ e0.0625 + 0.1225
e0.3025 + e0.4225
+ e0.2025
+
+ e0.5625 €0.7225 +0.9025]
The figure illustrates this approximation.
(b) Since f(x) = ex², we have f'(x)
=
0 ≤ f'(x) =
< 6e.
ASK YOUR TEACHER
and f'(x) =
Also, since 0 ≤ x ≤ 1 we have x² ≤
and so
Taking K = 6e, a = 0, b = 1, and n = 10 in the error estimate, we see that an upper bound for the error is as follows. (Round your final
answer to five decimal places.)
6e(1)3
e
24(
=
≈
Chapter 5 Solutions
Single Variable Calculus: Early Transcendentals, Volume I
Ch. 5.1 - Prob. 1ECh. 5.1 - (a) Use six rectangles to find estimates of each...Ch. 5.1 - (a) Estimate the area under the graph of f(x) =...Ch. 5.1 - Prob. 4ECh. 5.1 - (a) Estimate the area under the graph of f(x) = 1...Ch. 5.1 - Prob. 6ECh. 5.1 - Prob. 7ECh. 5.1 - Prob. 8ECh. 5.1 - The speed of a runner increased steadily during...Ch. 5.1 - The table shows speedometer readings at 10-second...
Ch. 5.1 - Oil leaked from a tank at a rate of r(t) liters...Ch. 5.1 - When we estimate distances from velocity data, it...Ch. 5.1 - The velocity graph of a braking car is shown. Use...Ch. 5.1 - The velocity graph of a car accelerating from rest...Ch. 5.1 - In someone infected with measles, the virus level...Ch. 5.1 - The table shows the number of people per day who...Ch. 5.1 - Use Definition 2 to find an expression for the...Ch. 5.1 - Use Definition 2 to find an expression for the...Ch. 5.1 - Use Definition 2 to find an expression for the...Ch. 5.1 - Prob. 24ECh. 5.1 - Determine a region whose area is equal to the...Ch. 5.1 - Prob. 26ECh. 5.1 - Let A be the area under the graph of an increasing...Ch. 5.1 - Prob. 28ECh. 5.1 - (a) Let An be the area of a polygon with n equal...Ch. 5.2 - Evaluate the Riemann sum for f(x) = x 1, 6 x ...Ch. 5.2 - If f(x)=cosx0x3/4 evaluate the Riemann sum with n...Ch. 5.2 - If f(x) = x2 4, 0 x 3, find the Riemann sum...Ch. 5.2 - (a) Find the Riemann sum for f(x) = 1/x, 1 x 2,...Ch. 5.2 - The graph of a function f is given. Estimate...Ch. 5.2 - The graph of g is shown. Estimate 24g(x)dx with...Ch. 5.2 - A table of values of an increasing function f is...Ch. 5.2 - The table gives the values of a function obtained...Ch. 5.2 - Prob. 9ECh. 5.2 - Prob. 10ECh. 5.2 - Prob. 11ECh. 5.2 - Prob. 12ECh. 5.2 - Prob. 14ECh. 5.2 - Prob. 15ECh. 5.2 - Prob. 16ECh. 5.2 - Prob. 17ECh. 5.2 - Prob. 18ECh. 5.2 - Prob. 19ECh. 5.2 - Express the limit as a definite integral on the...Ch. 5.2 - Prob. 21ECh. 5.2 - Prob. 22ECh. 5.2 - Prob. 23ECh. 5.2 - Prob. 24ECh. 5.2 - Prob. 25ECh. 5.2 - (a) Find an approximation to the integral...Ch. 5.2 - Prob. 27ECh. 5.2 - Prob. 28ECh. 5.2 - Prob. 29ECh. 5.2 - Prob. 30ECh. 5.2 - The graph of f is shown. Evaluate each integral by...Ch. 5.2 - The graph of g consists of two straight lines and...Ch. 5.2 - Prob. 35ECh. 5.2 - Prob. 36ECh. 5.2 - Prob. 37ECh. 5.2 - Prob. 38ECh. 5.2 - Prob. 39ECh. 5.2 - Prob. 40ECh. 5.2 - Prob. 41ECh. 5.2 - Prob. 42ECh. 5.2 - Prob. 43ECh. 5.2 - Prob. 44ECh. 5.2 - Prob. 45ECh. 5.2 - Prob. 46ECh. 5.2 - Prob. 47ECh. 5.2 - Prob. 48ECh. 5.2 - Prob. 49ECh. 5.2 - Prob. 50ECh. 5.2 - Prob. 51ECh. 5.2 - Prob. 52ECh. 5.2 - Each of the regions A, B, and C bounded by the...Ch. 5.2 - Prob. 54ECh. 5.2 - Prob. 55ECh. 5.2 - Prob. 56ECh. 5.2 - Prob. 57ECh. 5.2 - Use the properties of integrals to verify the...Ch. 5.2 - Prob. 59ECh. 5.2 - Prob. 60ECh. 5.2 - Prob. 61ECh. 5.2 - Prob. 62ECh. 5.2 - Prob. 63ECh. 5.2 - Prob. 64ECh. 5.2 - Prob. 65ECh. 5.2 - Prob. 66ECh. 5.2 - Prob. 67ECh. 5.2 - Prob. 68ECh. 5.2 - Prob. 69ECh. 5.2 - Prob. 70ECh. 5.2 - Prob. 71ECh. 5.2 - Prob. 72ECh. 5.2 - Prob. 73ECh. 5.2 - Express the limit as a definite integral....Ch. 5.2 - Find 12x2dx. Hint: Choose xi to be the geometric...Ch. 5.3 - Explain exactly what is meant by the statement...Ch. 5.3 - Prob. 2ECh. 5.3 - Prob. 3ECh. 5.3 - Prob. 4ECh. 5.3 - Prob. 5ECh. 5.3 - Prob. 6ECh. 5.3 - Prob. 7ECh. 5.3 - Prob. 8ECh. 5.3 - Prob. 9ECh. 5.3 - Prob. 10ECh. 5.3 - Prob. 11ECh. 5.3 - Prob. 12ECh. 5.3 - Prob. 13ECh. 5.3 - Prob. 14ECh. 5.3 - Prob. 15ECh. 5.3 - Prob. 16ECh. 5.3 - Prob. 17ECh. 5.3 - Prob. 18ECh. 5.3 - Prob. 19ECh. 5.3 - Prob. 20ECh. 5.3 - Prob. 21ECh. 5.3 - Prob. 22ECh. 5.3 - Prob. 23ECh. 5.3 - Prob. 24ECh. 5.3 - Prob. 25ECh. 5.3 - Prob. 26ECh. 5.3 - Prob. 27ECh. 5.3 - Prob. 28ECh. 5.3 - Prob. 29ECh. 5.3 - Prob. 30ECh. 5.3 - Prob. 31ECh. 5.3 - Prob. 32ECh. 5.3 - Prob. 33ECh. 5.3 - Prob. 34ECh. 5.3 - Prob. 35ECh. 5.3 - Prob. 36ECh. 5.3 - Prob. 37ECh. 5.3 - Prob. 38ECh. 5.3 - Prob. 39ECh. 5.3 - Prob. 40ECh. 5.3 - Prob. 41ECh. 5.3 - Prob. 42ECh. 5.3 - Prob. 43ECh. 5.3 - Prob. 44ECh. 5.3 - Prob. 45ECh. 5.3 - Sketch the region enclosed by the given curves and...Ch. 5.3 - Sketch the region enclosed by the given curves and...Ch. 5.3 - Prob. 48ECh. 5.3 - Use a graph to give a rough estimate of the area...Ch. 5.3 - Prob. 50ECh. 5.3 - Prob. 51ECh. 5.3 - Prob. 52ECh. 5.3 - Prob. 53ECh. 5.3 - Prob. 54ECh. 5.3 - Prob. 55ECh. 5.3 - Prob. 56ECh. 5.3 - Prob. 57ECh. 5.3 - What is wrong with the equation? 0sec2xdx=tanx]0=0Ch. 5.3 - Prob. 59ECh. 5.3 - Prob. 60ECh. 5.3 - Prob. 61ECh. 5.3 - Prob. 62ECh. 5.3 - Prob. 63ECh. 5.3 - Prob. 64ECh. 5.3 - Prob. 65ECh. 5.3 - Prob. 66ECh. 5.3 - Prob. 67ECh. 5.3 - Prob. 68ECh. 5.3 - If f(1) = 12, f is continuous, and 14f(x)dx=17,...Ch. 5.3 - Prob. 70ECh. 5.3 - Prob. 73ECh. 5.3 - Prob. 74ECh. 5.3 - Evaluate the limit by first recognizing the sum as...Ch. 5.3 - Prob. 76ECh. 5.3 - Prob. 77ECh. 5.3 - Prob. 78ECh. 5.3 - Prob. 79ECh. 5.3 - (a) Show that cos(x2) cos x for 0 x 1. (b)...Ch. 5.3 - Show that 0510x2x4+x2+1dx0.1 by comparing the...Ch. 5.3 - Prob. 82ECh. 5.3 - Prob. 83ECh. 5.3 - The area labeled B is three times the area labeled...Ch. 5.3 - Prob. 85ECh. 5.3 - Prob. 86ECh. 5.4 - Prob. 1ECh. 5.4 - Prob. 2ECh. 5.4 - Prob. 3ECh. 5.4 - Prob. 4ECh. 5.4 - Find the general indefinite integral....Ch. 5.4 - Prob. 6ECh. 5.4 - Prob. 7ECh. 5.4 - Prob. 8ECh. 5.4 - Prob. 9ECh. 5.4 - Prob. 10ECh. 5.4 - Prob. 11ECh. 5.4 - Prob. 12ECh. 5.4 - Prob. 13ECh. 5.4 - Prob. 14ECh. 5.4 - Prob. 15ECh. 5.4 - Prob. 16ECh. 5.4 - Prob. 17ECh. 5.4 - Prob. 18ECh. 5.4 - Prob. 19ECh. 5.4 - Prob. 20ECh. 5.4 - Prob. 21ECh. 5.4 - Prob. 22ECh. 5.4 - Prob. 23ECh. 5.4 - Prob. 24ECh. 5.4 - Prob. 25ECh. 5.4 - Prob. 26ECh. 5.4 - Prob. 27ECh. 5.4 - Prob. 28ECh. 5.4 - Prob. 29ECh. 5.4 - Prob. 30ECh. 5.4 - Prob. 31ECh. 5.4 - Evaluate the integral. 14yyy2dyCh. 5.4 - Prob. 33ECh. 5.4 - Prob. 34ECh. 5.4 - Prob. 35ECh. 5.4 - Prob. 36ECh. 5.4 - Prob. 37ECh. 5.4 - Prob. 38ECh. 5.4 - Prob. 39ECh. 5.4 - Prob. 40ECh. 5.4 - Prob. 41ECh. 5.4 - Prob. 42ECh. 5.4 - Prob. 43ECh. 5.4 - Prob. 44ECh. 5.4 - Prob. 45ECh. 5.4 - Prob. 46ECh. 5.4 - Prob. 47ECh. 5.4 - Prob. 48ECh. 5.4 - The area of the region that lies to the right of...Ch. 5.4 - The boundaries of the shaded region are the...Ch. 5.4 - Prob. 51ECh. 5.4 - Prob. 52ECh. 5.4 - If oil leaks from a tank at a rate of r(t) gallons...Ch. 5.4 - A honeybee population starts with 100 bees and...Ch. 5.4 - In Section 4.7 we defined the marginal revenue...Ch. 5.4 - If f(x) is the slope of a trail at a distance of x...Ch. 5.4 - Prob. 57ECh. 5.4 - Prob. 58ECh. 5.4 - Prob. 59ECh. 5.4 - Prob. 60ECh. 5.4 - Prob. 61ECh. 5.4 - The acceleration function (in m/s2) and the...Ch. 5.4 - Prob. 63ECh. 5.4 - Prob. 64ECh. 5.4 - Prob. 65ECh. 5.4 - Prob. 66ECh. 5.4 - Prob. 67ECh. 5.4 - Prob. 68ECh. 5.4 - Prob. 69ECh. 5.4 - Prob. 70ECh. 5.4 - A bacteria population is 4000 at time t = 0 and...Ch. 5.4 - Prob. 72ECh. 5.4 - Shown is the power consumption in the province of...Ch. 5.5 - Prob. 1ECh. 5.5 - Prob. 2ECh. 5.5 - Prob. 3ECh. 5.5 - Prob. 4ECh. 5.5 - Prob. 5ECh. 5.5 - Prob. 6ECh. 5.5 - Prob. 7ECh. 5.5 - Prob. 8ECh. 5.5 - Prob. 9ECh. 5.5 - Prob. 10ECh. 5.5 - Evaluate the indefinite integral. cos(t/2)dtCh. 5.5 - Prob. 12ECh. 5.5 - Prob. 13ECh. 5.5 - Prob. 14ECh. 5.5 - Prob. 15ECh. 5.5 - Prob. 16ECh. 5.5 - Prob. 17ECh. 5.5 - Prob. 18ECh. 5.5 - Prob. 19ECh. 5.5 - Prob. 20ECh. 5.5 - Prob. 21ECh. 5.5 - Prob. 22ECh. 5.5 - Prob. 23ECh. 5.5 - Prob. 24ECh. 5.5 - Prob. 25ECh. 5.5 - Prob. 26ECh. 5.5 - Prob. 27ECh. 5.5 - Prob. 28ECh. 5.5 - Evaluate the indefinite integral. 5tsin(5t)dtCh. 5.5 - Prob. 30ECh. 5.5 - Prob. 31ECh. 5.5 - Prob. 32ECh. 5.5 - Prob. 33ECh. 5.5 - Prob. 34ECh. 5.5 - Prob. 35ECh. 5.5 - Prob. 36ECh. 5.5 - Prob. 37ECh. 5.5 - Prob. 38ECh. 5.5 - Prob. 39ECh. 5.5 - Prob. 40ECh. 5.5 - Prob. 41ECh. 5.5 - Prob. 42ECh. 5.5 - Prob. 43ECh. 5.5 - Prob. 44ECh. 5.5 - Prob. 45ECh. 5.5 - Prob. 46ECh. 5.5 - Prob. 47ECh. 5.5 - Prob. 48ECh. 5.5 - Prob. 49ECh. 5.5 - Prob. 50ECh. 5.5 - Prob. 51ECh. 5.5 - Prob. 52ECh. 5.5 - Prob. 53ECh. 5.5 - Prob. 54ECh. 5.5 - Prob. 55ECh. 5.5 - Prob. 56ECh. 5.5 - Evaluate the definite integral. 0/6sintcos2tdtCh. 5.5 - Prob. 58ECh. 5.5 - Prob. 59ECh. 5.5 - Prob. 60ECh. 5.5 - Prob. 61ECh. 5.5 - Prob. 62ECh. 5.5 - Prob. 63ECh. 5.5 - Prob. 64ECh. 5.5 - Prob. 65ECh. 5.5 - Prob. 66ECh. 5.5 - Prob. 67ECh. 5.5 - Prob. 68ECh. 5.5 - Prob. 69ECh. 5.5 - Prob. 70ECh. 5.5 - Prob. 71ECh. 5.5 - Prob. 72ECh. 5.5 - Prob. 73ECh. 5.5 - Prob. 74ECh. 5.5 - Prob. 75ECh. 5.5 - Prob. 76ECh. 5.5 - Prob. 77ECh. 5.5 - Evaluate 01x1x4dx by making a substitution and...Ch. 5.5 - Which of the following areas are equal? Why?Ch. 5.5 - Prob. 80ECh. 5.5 - An oil storage tank ruptures at time t = 0 and oil...Ch. 5.5 - Prob. 82ECh. 5.5 - Prob. 83ECh. 5.5 - Prob. 84ECh. 5.5 - Dialysis treatment removes urea and other waste...Ch. 5.5 - Prob. 86ECh. 5.5 - Prob. 87ECh. 5.5 - Prob. 88ECh. 5.5 - If f is continuous on , prove that...Ch. 5.5 - Prob. 90ECh. 5.5 - Prob. 91ECh. 5.5 - Prob. 92ECh. 5.5 - Prob. 93ECh. 5.5 - Prob. 94ECh. 5 - (a) Write an expression for a Riemann sum of a...Ch. 5 - Prob. 2RCCCh. 5 - Prob. 3RCCCh. 5 - Prob. 4RCCCh. 5 - Prob. 5RCCCh. 5 - Suppose a particle moves back and forth along a...Ch. 5 - Prob. 7RCCCh. 5 - Prob. 8RCCCh. 5 - Prob. 9RCCCh. 5 - Prob. 1RQCh. 5 - Prob. 2RQCh. 5 - Prob. 3RQCh. 5 - Prob. 4RQCh. 5 - Prob. 5RQCh. 5 - Prob. 6RQCh. 5 - Prob. 7RQCh. 5 - Prob. 8RQCh. 5 - Prob. 9RQCh. 5 - Prob. 10RQCh. 5 - Prob. 11RQCh. 5 - Prob. 12RQCh. 5 - Prob. 13RQCh. 5 - Prob. 14RQCh. 5 - Prob. 15RQCh. 5 - Prob. 16RQCh. 5 - Prob. 17RQCh. 5 - Prob. 18RQCh. 5 - Use the given graph of f to find the Riemann sum...Ch. 5 - Prob. 2RECh. 5 - Prob. 3RECh. 5 - Prob. 4RECh. 5 - Prob. 5RECh. 5 - Prob. 6RECh. 5 - Prob. 7RECh. 5 - Evaluate: (a) 01ddx(earctanx)dx (b)...Ch. 5 - Prob. 9RECh. 5 - Prob. 10RECh. 5 - Prob. 11RECh. 5 - Prob. 12RECh. 5 - Prob. 13RECh. 5 - Prob. 14RECh. 5 - Prob. 15RECh. 5 - Prob. 16RECh. 5 - Prob. 17RECh. 5 - Prob. 18RECh. 5 - Prob. 19RECh. 5 - Prob. 20RECh. 5 - Prob. 21RECh. 5 - Prob. 22RECh. 5 - Prob. 23RECh. 5 - Prob. 24RECh. 5 - Prob. 25RECh. 5 - Prob. 26RECh. 5 - Prob. 27RECh. 5 - Prob. 28RECh. 5 - Prob. 29RECh. 5 - Prob. 30RECh. 5 - Prob. 31RECh. 5 - Prob. 32RECh. 5 - Prob. 33RECh. 5 - Prob. 34RECh. 5 - Prob. 35RECh. 5 - Prob. 36RECh. 5 - Prob. 37RECh. 5 - Prob. 38RECh. 5 - Prob. 39RECh. 5 - Prob. 40RECh. 5 - Prob. 41RECh. 5 - Prob. 42RECh. 5 - Prob. 43RECh. 5 - Prob. 44RECh. 5 - Prob. 45RECh. 5 - Prob. 46RECh. 5 - Prob. 47RECh. 5 - Prob. 48RECh. 5 - Prob. 49RECh. 5 - Prob. 50RECh. 5 - Prob. 51RECh. 5 - Use Property 8 of integrals to estimate the value...Ch. 5 - Prob. 53RECh. 5 - Prob. 54RECh. 5 - Prob. 55RECh. 5 - Use the properties of integrals to verify the...Ch. 5 - Use the Midpoint Rule with n = 6 to approximate...Ch. 5 - Prob. 58RECh. 5 - Prob. 59RECh. 5 - A radar gun was used to record the speed of a...Ch. 5 - Prob. 61RECh. 5 - Prob. 62RECh. 5 - Prob. 63RECh. 5 - Prob. 66RECh. 5 - Prob. 69RECh. 5 - Prob. 70RECh. 5 - Prob. 71RECh. 5 - Prob. 72RECh. 5 - Prob. 1PCh. 5 - Prob. 2PCh. 5 - Prob. 3PCh. 5 - Prob. 5PCh. 5 - Prob. 6PCh. 5 - Prob. 7PCh. 5 - The figure shows two regions in the first...Ch. 5 - Prob. 9PCh. 5 - Prob. 10PCh. 5 - Prob. 11PCh. 5 - Prob. 14PCh. 5 - Prob. 15PCh. 5 - Prob. 18PCh. 5 - Prob. 19P
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