Student Solutions Manual, Chapters 1-11 for Stewart's Single Variable Calculus, 8th (James Stewart Calculus)
8th Edition
ISBN: 9781305271814
Author: James Stewart
Publisher: Cengage Learning
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Textbook Question
Chapter 4.1, Problem 9E
With a programmable calculator (or a computer), it is possible to evaluate the expressions for the sums of areas of approximating rectangles, even for large values of n, using looping. (On a TI use the Is > command or a For-EndFor loop, on a Casio use Isz, on an HP or in BASIC use a FOR-NEXT loop.) Compute the sum of the areas of approximating rectangles using equal subintervals and right endpoints for n = 10, 30, 50, and 100. Then guess the value of the exact area.
9. The region under y = x4 from 0 to 1
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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(
=
≈
2. [-/1 Points]
DETAILS
MY NOTES
SESSCALCET2 6.5.015.
Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.)
ASK YOUR TEACHER
3
1
3 +
dy, n = 6
(a) the Trapezoidal Rule
(b) the Midpoint Rule
(c) Simpson's Rule
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Chapter 4 Solutions
Student Solutions Manual, Chapters 1-11 for Stewart's Single Variable Calculus, 8th (James Stewart Calculus)
Ch. 4.1 - Prob. 1ECh. 4.1 - (a) Use six rectangles to find estimates of each...Ch. 4.1 - (a) Estimate the area under the graph of f(x) =...Ch. 4.1 - Prob. 4ECh. 4.1 - (a) Estimate the area under the graph of f(x) = 1...Ch. 4.1 - Prob. 6ECh. 4.1 - Prob. 7ECh. 4.1 - Prob. 8ECh. 4.1 - With a programmable calculator (or a computer), it...Ch. 4.1 - With a programmable calculator (or a computer), it...
Ch. 4.1 - Prob. 11ECh. 4.1 - Prob. 12ECh. 4.1 - The speed of a runner increased steadily during...Ch. 4.1 - Prob. 14ECh. 4.1 - Oil leaked from a tank at a rate of r(t) liters...Ch. 4.1 - Prob. 16ECh. 4.1 - The velocity graph of a braking car is shown. Use...Ch. 4.1 - The velocity graph of a car accelerating from rest...Ch. 4.1 - In someone infected with measles, the virus level...Ch. 4.1 - The table shows the number of people per day who...Ch. 4.1 - Use Definition 2 to find an expression for the...Ch. 4.1 - Prob. 22ECh. 4.1 - Use Definition 2 to find an expression for the...Ch. 4.1 - Prob. 24ECh. 4.1 - Prob. 25ECh. 4.1 - (a) Use Definition 2 to find an expression for the...Ch. 4.1 - Let A be the area under the graph of an increasing...Ch. 4.1 - If A is the area under the curve y = sin x from 0...Ch. 4.1 - (a) Express the area under the curve y = x5 from 0...Ch. 4.1 - (a) Express the area under the curve y = x4 + 5x2...Ch. 4.1 - Prob. 31ECh. 4.1 - (a) Let An be the area of a polygon with n equal...Ch. 4.2 - Evaluate the Riemann sum for f(x)=x1,6x4, with...Ch. 4.2 - If f(x)=cosx0x3/4 evaluate the Riemann sum with n...Ch. 4.2 - If f(x)=x24,0x3, find the Riemann sum with n = 6,...Ch. 4.2 - (a) Find the Riemann sum for f(x)=1/x,1x2, with...Ch. 4.2 - The graph of a function f is given. Estimate...Ch. 4.2 - The graph of g is shown. Estimate 24g(x)dx with...Ch. 4.2 - A table of values of an increasing function f is...Ch. 4.2 - Prob. 8ECh. 4.2 - Prob. 9ECh. 4.2 - Prob. 10ECh. 4.2 - Prob. 11ECh. 4.2 - Prob. 12ECh. 4.2 - If you have a CAS that evaluates midpoint...Ch. 4.2 - Prob. 14ECh. 4.2 - Prob. 15ECh. 4.2 - Prob. 16ECh. 4.2 - Express the limit as a definite integral on the...Ch. 4.2 - Express the limit as a definite integral on the...Ch. 4.2 - Express the limit as a definite integral on the...Ch. 4.2 - Prob. 20ECh. 4.2 - Use the form of the definition of the integral...Ch. 4.2 - Use the form of the definition of the integral...Ch. 4.2 - Use the form of the definition of the integral...Ch. 4.2 - Use the form of the definition of the integral...Ch. 4.2 - Use the form of the definition of the integral...Ch. 4.2 - Prob. 26ECh. 4.2 - Prove that abxdx=b2a22.Ch. 4.2 - Prob. 28ECh. 4.2 - Prob. 29ECh. 4.2 - Prob. 30ECh. 4.2 - Express the integral as a limit of sums. Then...Ch. 4.2 - Prob. 32ECh. 4.2 - The graph of f is shown. Evaluate each integral by...Ch. 4.2 - The graph of g consists of two straight lines and...Ch. 4.2 - Evaluate the integral by interpreting it in terms...Ch. 4.2 - Evaluate the integral by interpreting it in terms...Ch. 4.2 - Evaluate the integral by interpreting it in terms...Ch. 4.2 - Evaluate the integral by interpreting it in terms...Ch. 4.2 - Prob. 39ECh. 4.2 - Evaluate the integral by interpreting it in terms...Ch. 4.2 - Prob. 41ECh. 4.2 - Give that 0sin4xdx=38, what is 0sin4d?Ch. 4.2 - In Example 4.1.2 we showed that 01x2dx=13. Use...Ch. 4.2 - Prob. 44ECh. 4.2 - Prob. 45ECh. 4.2 - Prob. 46ECh. 4.2 - Prob. 47ECh. 4.2 - If 28f(x)dx=7.3 and 24f(x)dx=5.9, find 48f(x)dx.Ch. 4.2 - Prob. 49ECh. 4.2 - Prob. 50ECh. 4.2 - Prob. 51ECh. 4.2 - Prob. 52ECh. 4.2 - Prob. 53ECh. 4.2 - Suppose f has absolute minimum value m and...Ch. 4.2 - Prob. 55ECh. 4.2 - Prob. 56ECh. 4.2 - Use the properties of integrals to verify the...Ch. 4.2 - Prob. 58ECh. 4.2 - Prob. 59ECh. 4.2 - Prob. 60ECh. 4.2 - Prob. 61ECh. 4.2 - Prob. 62ECh. 4.2 - Prob. 63ECh. 4.2 - Prob. 64ECh. 4.2 - Prob. 65ECh. 4.2 - Prob. 66ECh. 4.2 - Prob. 67ECh. 4.2 - Prob. 68ECh. 4.2 - Prob. 69ECh. 4.2 - Prob. 70ECh. 4.2 - Prob. 71ECh. 4.2 - Prob. 72ECh. 4.2 - Express the limit as a definite integral. 73....Ch. 4.2 - Prob. 74ECh. 4.2 - Prob. 75ECh. 4.3 - Explain exactly what is meant by the statement...Ch. 4.3 - Prob. 2ECh. 4.3 - Let g(x)=0xf(t)dt, where f is the function whose...Ch. 4.3 - Prob. 4ECh. 4.3 - Sketch the area represented by g(x). Then find...Ch. 4.3 - Prob. 6ECh. 4.3 - Use Part 1 of the Fundamental Theorem of Calculus...Ch. 4.3 - Prob. 8ECh. 4.3 - Use Part 1 of the Fundamental Theorem of Calculus...Ch. 4.3 - Prob. 10ECh. 4.3 - Use Part 1 of the Fundamental Theorem of Calculus...Ch. 4.3 - Prob. 12ECh. 4.3 - Use Part 1 of the Fundamental Theorem of Calculus...Ch. 4.3 - Use Part 1 of the Fundamental Theorem of Calculus...Ch. 4.3 - Use Part 1 of the Fundamental Theorem of Calculus...Ch. 4.3 - Prob. 16ECh. 4.3 - Use Part 1 of the Fundamental Theorem of Calculus...Ch. 4.3 - Prob. 18ECh. 4.3 - Evaluate the integral. 19. 13(x2+2x4)dxCh. 4.3 - Prob. 20ECh. 4.3 - Prob. 21ECh. 4.3 - Prob. 22ECh. 4.3 - Evaluate the integral. 23. 19xdxCh. 4.3 - Prob. 24ECh. 4.3 - Evaluate the integral. 25. /6sindCh. 4.3 - Prob. 26ECh. 4.3 - Evaluate the integral. 27. 01(u+2)(u3)duCh. 4.3 - Prob. 28ECh. 4.3 - Evaluate the integral. 29. 142+x2xdxCh. 4.3 - Prob. 30ECh. 4.3 - Evaluate the integral. 31. /6/2csctcottdtCh. 4.3 - Prob. 32ECh. 4.3 - Prob. 33ECh. 4.3 - Prob. 34ECh. 4.3 - Evaluate the integral. 35. 12v5+3v6v4dvCh. 4.3 - Prob. 36ECh. 4.3 - Prob. 37ECh. 4.3 - Prob. 38ECh. 4.3 - Prob. 39ECh. 4.3 - Prob. 40ECh. 4.3 - Prob. 41ECh. 4.3 - Prob. 42ECh. 4.3 - Use a graph to give a rough estimate of the area...Ch. 4.3 - Prob. 44ECh. 4.3 - Prob. 45ECh. 4.3 - Use a graph to give a rough estimate of the area...Ch. 4.3 - Prob. 47ECh. 4.3 - Prob. 48ECh. 4.3 - Prob. 49ECh. 4.3 - Prob. 50ECh. 4.3 - Prob. 51ECh. 4.3 - Prob. 52ECh. 4.3 - Prob. 53ECh. 4.3 - Prob. 54ECh. 4.3 - Prob. 55ECh. 4.3 - Prob. 56ECh. 4.3 - Prob. 57ECh. 4.3 - If f(x)=0x(1t2)cos2tdt, on what interval is f...Ch. 4.3 - On what interval is the curve y=0xt2t2+t+2dt...Ch. 4.3 - Prob. 60ECh. 4.3 - Prob. 61ECh. 4.3 - Prob. 62ECh. 4.3 - The Fresnel function S was defined in Example 3...Ch. 4.3 - The sine integral function Si(x)=0xsinttdt is...Ch. 4.3 - Let g(x)=0xf(t)dt, where f is the function whose...Ch. 4.3 - Let g(x)=0xf(t)dt, where f is the function whose...Ch. 4.3 - Prob. 67ECh. 4.3 - Prob. 68ECh. 4.3 - Prob. 69ECh. 4.3 - Prob. 70ECh. 4.3 - Prob. 71ECh. 4.3 - (a) Show that cos(x2) cos x for 0 x 1. (b)...Ch. 4.3 - Show that 0510x2x4+x2+1dx0.1 by comparing the...Ch. 4.3 - Let f(x)={0ifx0xif0x12xif1x20ifx2 and...Ch. 4.3 - Find a function f and a number a such that...Ch. 4.3 - Prob. 76ECh. 4.3 - A manufacturing company owns a major piece of...Ch. 4.3 - A high-tech company purchases a new computing...Ch. 4.3 - Evaluate the integral. 79. 1912xdxCh. 4.3 - Prob. 80ECh. 4.3 - Prob. 81ECh. 4.3 - Prob. 82ECh. 4.3 - Prob. 83ECh. 4.3 - Prob. 84ECh. 4.4 - Verify by differentiation that the formula is...Ch. 4.4 - Verify by differentiation that the formula is...Ch. 4.4 - Prob. 3ECh. 4.4 - Prob. 4ECh. 4.4 - Find the general indefinite integral. 5....Ch. 4.4 - Prob. 6ECh. 4.4 - Find the general indefinite integral. 7....Ch. 4.4 - Prob. 8ECh. 4.4 - Find the general indefinite integral. 9....Ch. 4.4 - Prob. 10ECh. 4.4 - Find the general indefinite integral. 11. 1+x+xxdxCh. 4.4 - Prob. 12ECh. 4.4 - Find the general indefinite integral. 13....Ch. 4.4 - Prob. 14ECh. 4.4 - Find the general indefinite integral. 15....Ch. 4.4 - Prob. 16ECh. 4.4 - Find the general indefinite integral. Illustrate...Ch. 4.4 - Prob. 18ECh. 4.4 - Evaluate the integral. 19. 23(x23)dxCh. 4.4 - Prob. 20ECh. 4.4 - Evaluate the integral. 21. 20(12t4+14t3t)dtCh. 4.4 - Prob. 22ECh. 4.4 - Evaluate the integral. 23. 02(2x3)(4x2+1)dxCh. 4.4 - Prob. 24ECh. 4.4 - Evaluate the integral. 25. 0(4sin3cos)dCh. 4.4 - Prob. 26ECh. 4.4 - Prob. 27ECh. 4.4 - Prob. 28ECh. 4.4 - Prob. 29ECh. 4.4 - Prob. 30ECh. 4.4 - Prob. 31ECh. 4.4 - Prob. 32ECh. 4.4 - Prob. 33ECh. 4.4 - Prob. 34ECh. 4.4 - Prob. 35ECh. 4.4 - Prob. 36ECh. 4.4 - Prob. 37ECh. 4.4 - Prob. 38ECh. 4.4 - Prob. 39ECh. 4.4 - Prob. 40ECh. 4.4 - Prob. 41ECh. 4.4 - Prob. 42ECh. 4.4 - Prob. 43ECh. 4.4 - Repeat Exercise 43 for the curve y = 2x + 3x4 ...Ch. 4.4 - The area of the region that lies to the right of...Ch. 4.4 - Prob. 46ECh. 4.4 - If w'(t) is the rate of growth of a child in...Ch. 4.4 - Prob. 48ECh. 4.4 - If oil leaks from a tank at a rate of r(t) gallons...Ch. 4.4 - A honeybee population starts with 100 bees and...Ch. 4.4 - In Section 3.7 we defined the marginal revenue...Ch. 4.4 - Prob. 52ECh. 4.4 - If x is measured in meters and f(x) is measured in...Ch. 4.4 - If the units for x are feet and the units for a(x)...Ch. 4.4 - The velocity function (in meters per second) is...Ch. 4.4 - The velocity function (in meters per second) is...Ch. 4.4 - Prob. 57ECh. 4.4 - Prob. 58ECh. 4.4 - The linear density of a rod of length 4 m is given...Ch. 4.4 - Water flows from the bottom of a storage tank at a...Ch. 4.4 - Prob. 61ECh. 4.4 - Suppose that a volcano is erupting and readings of...Ch. 4.4 - Prob. 63ECh. 4.4 - Prob. 64ECh. 4.4 - The graph of the acceleration a(t) of a car...Ch. 4.4 - Shown is the graph of traffic on an Internet...Ch. 4.4 - The following graph shows the power consumption in...Ch. 4.4 - Prob. 68ECh. 4.4 - Evaluate the integral. 69. (sinx+sinhx)dxCh. 4.4 - Prob. 70ECh. 4.4 - Prob. 71ECh. 4.4 - Prob. 72ECh. 4.4 - Prob. 73ECh. 4.4 - The area labeled B is three times the area labeled...Ch. 4.5 - Evaluate the integral by making the given...Ch. 4.5 - Prob. 2ECh. 4.5 - Evaluate the integral by making the given...Ch. 4.5 - Prob. 4ECh. 4.5 - Evaluate the integral by making the given...Ch. 4.5 - Prob. 6ECh. 4.5 - Evaluate the indefinite integral. 7. x1x2dxCh. 4.5 - Prob. 8ECh. 4.5 - Evaluate the indefinite integral. 9. (12x)9dxCh. 4.5 - Prob. 10ECh. 4.5 - Evaluate the indefinite integral. 11. sin(2/3)dCh. 4.5 - Prob. 12ECh. 4.5 - Evaluate the indefinite integral. 13. sec3ttan3tdtCh. 4.5 - Prob. 14ECh. 4.5 - Evaluate the indefinite integral. 15. cos(1+5t)dtCh. 4.5 - Prob. 16ECh. 4.5 - Evaluate the indefinite integral. 17. sec2tan3dCh. 4.5 - Prob. 18ECh. 4.5 - Evaluate the indefinite integral. 19....Ch. 4.5 - Prob. 20ECh. 4.5 - Prob. 21ECh. 4.5 - Evaluate the indefinite integral. 22. cos(/x)x2dxCh. 4.5 - Evaluate the indefinite integral. 23. z21+z33dzCh. 4.5 - Prob. 24ECh. 4.5 - Evaluate the indefinite integral. 25. cotxcsc2xdxCh. 4.5 - Prob. 26ECh. 4.5 - Evaluate the indefinite integral. 27. sec3xtanxdxCh. 4.5 - Prob. 28ECh. 4.5 - Evaluate the indefinite integral. 29. x(2x+5)8dxCh. 4.5 - Prob. 30ECh. 4.5 - Prob. 31ECh. 4.5 - Prob. 32ECh. 4.5 - Prob. 33ECh. 4.5 - Prob. 34ECh. 4.5 - Evaluate the definite integral. 35. 01cos(t/2)dtCh. 4.5 - Prob. 36ECh. 4.5 - Evaluate the definite integral. 37. 011+7x3dxCh. 4.5 - Prob. 38ECh. 4.5 - Prob. 39ECh. 4.5 - Prob. 40ECh. 4.5 - Prob. 41ECh. 4.5 - Prob. 42ECh. 4.5 - Evaluate the definite integral. 43. 013dx(1+2x)23Ch. 4.5 - Prob. 44ECh. 4.5 - Evaluate the definite integral. 45. 0axx2+a2dx(a0)Ch. 4.5 - Prob. 46ECh. 4.5 - Evaluate the definite integral. 47. 12xx1dxCh. 4.5 - Prob. 48ECh. 4.5 - Evaluate the definite integral. 49....Ch. 4.5 - Prob. 50ECh. 4.5 - Prob. 51ECh. 4.5 - Prob. 52ECh. 4.5 - Use a graph to give a rough estimate of the area...Ch. 4.5 - Use a graph to give a rough estimate of the area...Ch. 4.5 - Prob. 55ECh. 4.5 - Prob. 56ECh. 4.5 - Breathing is cyclic and a full respiratory cycle...Ch. 4.5 - A model for the basal metabolism rate, in kcal/h,...Ch. 4.5 - Prob. 59ECh. 4.5 - Prob. 60ECh. 4.5 - Prob. 61ECh. 4.5 - Prob. 62ECh. 4.5 - If a and b are positive numbers, show that...Ch. 4.5 - If f is continuous on [0, ], use the substitution...Ch. 4.5 - If f is continuous, prove that...Ch. 4.5 - Prob. 66ECh. 4.5 - Prob. 67ECh. 4.5 - Prob. 68ECh. 4.5 - Prob. 69ECh. 4.5 - Prob. 70ECh. 4.5 - Prob. 71ECh. 4.5 - Prob. 72ECh. 4.5 - Prob. 73ECh. 4.5 - Prob. 74ECh. 4.5 - Prob. 75ECh. 4.5 - Evaluate the integral. 76. sin(lnx)xdxCh. 4.5 - Prob. 77ECh. 4.5 - Prob. 78ECh. 4.5 - Prob. 79ECh. 4.5 - Prob. 80ECh. 4.5 - Prob. 81ECh. 4.5 - Prob. 82ECh. 4.5 - Evaluate the integral. 83. 01ez+1ez+zdzCh. 4.5 - Prob. 84ECh. 4.5 - Prob. 85ECh. 4 - (a) Write an expression for a Riemann sum of a...Ch. 4 - (a) Write the definition of the definite integral...Ch. 4 - State the Midpoint Rule.Ch. 4 - State both parts of the Fundamental Theorem of...Ch. 4 - (a) State the Net Change Theorem. (b) If r(t) is...Ch. 4 - Suppose a particle moves back and forth along a...Ch. 4 - Prob. 7RCCCh. 4 - Explain exactly what is meant by the statement...Ch. 4 - Prob. 9RCCCh. 4 - Prob. 1RQCh. 4 - Prob. 2RQCh. 4 - Prob. 3RQCh. 4 - Prob. 4RQCh. 4 - Prob. 5RQCh. 4 - Prob. 6RQCh. 4 - Prob. 7RQCh. 4 - Prob. 8RQCh. 4 - Prob. 9RQCh. 4 - Determine whether the statement is true or false....Ch. 4 - Prob. 11RQCh. 4 - Prob. 12RQCh. 4 - Prob. 13RQCh. 4 - Prob. 14RQCh. 4 - Prob. 15RQCh. 4 - Prob. 16RQCh. 4 - Prob. 17RQCh. 4 - Determine whether the statement is true or false....Ch. 4 - Use the given graph of f to find the Riemann sum...Ch. 4 - Prob. 2RECh. 4 - Prob. 3RECh. 4 - Prob. 4RECh. 4 - Prob. 5RECh. 4 - Prob. 6RECh. 4 - The figure shows the graphs of f,f, and 0xf(t)dt....Ch. 4 - Evaluate: (a) 0/2ddx(sinx2cosx3)dx (b)...Ch. 4 - Prob. 9RECh. 4 - Prob. 10RECh. 4 - Prob. 11RECh. 4 - Prob. 12RECh. 4 - Prob. 13RECh. 4 - Prob. 14RECh. 4 - Prob. 15RECh. 4 - Prob. 16RECh. 4 - Prob. 17RECh. 4 - Prob. 18RECh. 4 - Prob. 19RECh. 4 - Prob. 20RECh. 4 - Prob. 21RECh. 4 - Prob. 22RECh. 4 - Prob. 23RECh. 4 - Prob. 24RECh. 4 - Prob. 25RECh. 4 - Prob. 26RECh. 4 - Prob. 27RECh. 4 - Prob. 28RECh. 4 - Prob. 29RECh. 4 - Prob. 30RECh. 4 - Prob. 31RECh. 4 - Prob. 32RECh. 4 - Prob. 33RECh. 4 - Prob. 34RECh. 4 - Prob. 35RECh. 4 - Prob. 36RECh. 4 - Prob. 37RECh. 4 - Prob. 38RECh. 4 - Prob. 39RECh. 4 - Prob. 40RECh. 4 - Prob. 41RECh. 4 - Prob. 42RECh. 4 - Prob. 43RECh. 4 - Prob. 44RECh. 4 - Prob. 45RECh. 4 - A particle moves along a line with velocity...Ch. 4 - Prob. 47RECh. 4 - Prob. 48RECh. 4 - A population of honeybees increased at a rate of...Ch. 4 - Prob. 50RECh. 4 - If f is continuous and 02f(x)dx=6, evaluate...Ch. 4 - The Fresnel function S(x)=0xsin(12t2)dt was...Ch. 4 - Prob. 53RECh. 4 - Prob. 54RECh. 4 - Prob. 55RECh. 4 - Prob. 56RECh. 4 - If f is continuous on [0, 1], prove that...Ch. 4 - Prob. 58RECh. 4 - Prob. 1PCh. 4 - Prob. 2PCh. 4 - Prob. 3PCh. 4 - (a) Graph several members of the family of...Ch. 4 - Prob. 5PCh. 4 - If f(x)=0xx2sin(t2)dt, find f(x).Ch. 4 - Prob. 7PCh. 4 - Prob. 8PCh. 4 - Prob. 9PCh. 4 - Find d2dx20x(1sint1+u4du)dt.Ch. 4 - Suppose the coefficients of the cubic polynomial...Ch. 4 - Prob. 12PCh. 4 - Prob. 13PCh. 4 - The figure shows a parabolic segment, that is. a...Ch. 4 - Prob. 15PCh. 4 - Prob. 16PCh. 4 - Evaluate limn(1nn+1+1nn+2++1nn+n).Ch. 4 - For any number c, we let fc(x) be the smaller of...
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- 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. 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(3πt) (b) Write a formula for the slope of the tangent line to the circle at the point A at time t seconds: -cot (3πt) (c) Express the x-coordinate of the right end of the rod at point B as a function of t: 2 cos(3πt) +41/1 (d) Express the slope of the rod…arrow_forward4. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.5.024. Find the approximations Tη, Mn, and S, to the integral computer algebra system.) ASK YOUR TEACHER PRACTICE ANOTHER 4 39 √ dx for n = 6 and 12. Then compute the corresponding errors ET, EM, and Es. (Round your answers to six decimal places. You may wish to use the sum command on a n Tn Mn Sp 6 12 n ET EM Es 6 12 What observations can you make? In particular, what happens to the errors when n is doubled? As n is doubled, ET and EM are decreased by a factor of about Need Help? Read It ' and Es is decreased by a factor of aboutarrow_forward6. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.5.001. ASK YOUR TEACHER PRACTICE ANOTHER Let I = 4 f(x) dx, where f is the function whose graph is shown. = √ ² F(x 12 4 y f 1 2 (a) Use the graph to find L2, R2 and M2. 42 = R₂ = M₂ = 1 x 3 4arrow_forward
- practice problem please help!arrow_forwardFind a parameterization for a circle of radius 4 with center (-4,-6,-3) in a plane parallel to the yz plane. Write your parameterization so the y component includes a positive cosine.arrow_forward~ exp(10). A 3. Claim number per policy is modelled by Poisson(A) with A sample x of N = 100 policies presents an average = 4 claims per policy. (i) Compute an a priory estimate of numbers of claims per policy. [2 Marks] (ii) Determine the posterior distribution of A. Give your argument. [5 Marks] (iii) Compute an a posteriori estimate of numbers of claims per policy. [3 Marks]arrow_forward
- 2. The size of a claim is modelled by F(a, λ) with a fixed a a maximum likelihood estimate of A given a sample x with a sample mean x = 11 = 121. Give [5 Marks]arrow_forwardRobbie Bearing Word Problems Angles name: Jocelyn date: 1/18 8K 2. A Delta airplane and an SouthWest airplane take off from an airport at the same time. The bearing from the airport to the Delta plane is 23° and the bearing to the SouthWest plane is 152°. Two hours later the Delta plane is 1,103 miles from the airport and the SouthWest plane is 1,156 miles from the airport. What is the distance between the two planes? What is the bearing from the Delta plane to the SouthWest plane? What is the bearing to the Delta plane from the SouthWest plane? Delta y SW Angles ThreeFourthsMe MATH 2arrow_forwardFind the derivative of the function. m(t) = -4t (6t7 - 1)6arrow_forward
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