Pearson eText for Calculus & Its Applications -- Instant Access (Pearson+)
15th Edition
ISBN: 9780137590728
Author: Larry Goldstein, David Lay
Publisher: PEARSON+
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Textbook Question
Chapter 9.3, Problem 14E
Evaluate the following definite
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Students have asked these similar questions
The cup on the 9th hole of a golf course is located dead center in the middle of a circular green which is 40 feet in radius. Your ball is located as in the picture below. The ball follows a straight line path and exits the green at the right-most edge. Assume the ball travels 8 ft/sec.
Introduce coordinates so that the cup is the origin of an xy-coordinate system and start by writing down the equations of the circle and the linear path of the ball. Provide numerical answers below with two decimal places of accuracy.
50 feet
green
ball
40 feet
9
cup
ball path
rough
(a) The x-coordinate of the position where the ball enters the green will be
(b) The ball will exit the green exactly
seconds after it is hit.
(c) Suppose that L is a line tangent to the boundary of the golf green and parallel to the path of the ball. Let Q be the point where the line is tangent to the circle. Notice that there are two possible positions for Q. Find the possible x-coordinates of Q:
smallest x-coordinate =…
Draw the unit circle and plot the point P=(8,2). Observe there are TWO lines tangent to the circle passing through the point P. Answer the questions below with 3 decimal places of accuracy.
P
L1
L
(a) The line L₁ is tangent to the unit circle at the point
(b) The tangent line L₁ has equation:
X +
(c) The line L₂ is tangent to the unit circle at the point (
(d) The tangent line 42 has equation:
y=
x +
).
What is a solution to a differential equation? We said that a differential equation is an equation that
describes the derivative, or derivatives, of a function that is unknown to us. By a solution to a differential
equation, we mean simply a function that satisfies this description.
2. Here is a differential equation which describes an unknown position function s(t):
ds
dt
318
4t+1,
ds
(a) To check that s(t) = 2t2 + t is a solution to this differential equation, calculate
you really do get 4t +1.
and check that
dt'
(b) Is s(t) = 2t2 +++ 4 also a solution to this differential equation?
(c) Is s(t)=2t2 + 3t also a solution to this differential equation?
ds
1
dt
(d) To find all possible solutions, start with the differential equation = 4t + 1, then move dt to the
right side of the equation by multiplying, and then integrate both sides. What do you get?
(e) Does this differential equation have a unique solution, or an infinite family of solutions?
Chapter 9 Solutions
Pearson eText for Calculus & Its Applications -- Instant Access (Pearson+)
Ch. 9.1 - (Review) Differentiate the following functions:...Ch. 9.1 - Use the substitution u=3x to determine e3/xx2dx.Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...
Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Figure 1 shows graphs of several functions f(x)...Ch. 9.1 - Figure 2 shows graphs of several functions f(x)...Ch. 9.1 - Determine the following integrals using the...Ch. 9.1 - Determine the following integrals using indicated...Ch. 9.1 - Determine the following integrals using the...Ch. 9.1 - Determine the following integrals using the...Ch. 9.1 - Determine the following integrals by making an...Ch. 9.1 - Prob. 44ECh. 9.1 - Prob. 45ECh. 9.1 - Determine the following integrals by making an...Ch. 9.1 - Prob. 47ECh. 9.1 - Prob. 48ECh. 9.1 - Determine the following integrals by making an...Ch. 9.1 - Prob. 50ECh. 9.1 - Prob. 51ECh. 9.1 - Prob. 52ECh. 9.1 - Determine 2x(x2+5)dx by making a substitution....Ch. 9.2 - Evaluate the following integral. xe3xdxCh. 9.2 - Evaluate the following integral. lnxdxCh. 9.2 - Evaluate the following integral. xe5xdxCh. 9.2 - Evaluate the following integral. xex2dxCh. 9.2 - Evaluate the following integral. x(x+7)4dxCh. 9.2 - Evaluate the following integral. x(2x+3)...Ch. 9.2 - Evaluate the following integral. xexdxCh. 9.2 - Evaluate the following integral. x2exdxCh. 9.2 - Evaluate the following integral. xx+1dxCh. 9.2 - Evaluate the following integral. x3+2xdxCh. 9.2 - Evaluate the following integral. e2x(13x)dxCh. 9.2 - Evaluate the following integral. (1+x)2e2xdxCh. 9.2 - Evaluate the following integral. 6xe3xdxCh. 9.2 - Evaluate the following integral. x+2e2xdxCh. 9.2 - Evaluate the following integral. xx+1dxCh. 9.2 - Evaluate the following integral. x2xdxCh. 9.2 - Evaluate the following integral. xlnxdxCh. 9.2 - Evaluate the following integral. x5lnxdxCh. 9.2 - Evaluate the following integral. xcosxdxCh. 9.2 - Evaluate the following integral. xsin8xdxCh. 9.2 - Evaluate the following integral. xln5xdxCh. 9.2 - Evaluate the following integral. x3lnxdxCh. 9.2 - Evaluate the following integral. lnx4dxCh. 9.2 - Evaluate the following integral. ln(lnx)xdxCh. 9.2 - Evaluate the following integral. x2exdxCh. 9.2 - Evaluate the following integral. lnx+1dxCh. 9.2 - Evaluate the following integral using techniques...Ch. 9.2 - Evaluate the following integral using techniques...Ch. 9.2 - Evaluate the following integral using techniques...Ch. 9.2 - Evaluate the following integral using techniques...Ch. 9.2 - Evaluate the following integral using techniques...Ch. 9.2 - Evaluate the following integral using techniques...Ch. 9.2 - Evaluate the following integral using techniques...Ch. 9.2 - Evaluate the following integral using techniques...Ch. 9.2 - Evaluate the following integral using techniques...Ch. 9.2 - Evaluate the following integral using techniques...Ch. 9.2 - Evaluate the following integral using techniques...Ch. 9.2 - Evaluate the following integral using techniques...Ch. 9.2 - Figure 1 shows graphs of several functions f(x)...Ch. 9.2 - Figure 2 shows graphs of several functions f(x)...Ch. 9.2 - Evaluate xex(x+1)2dx using integration by parts....Ch. 9.2 - Evaluate x7ex4dx. [Hint: First, make a...Ch. 9.3 - Evaluate the following definite integrals:...Ch. 9.3 - Evaluate the following definite integrals:...Ch. 9.3 - Evaluate the following definite integrals:...Ch. 9.3 - Evaluate the following definite integrals:...Ch. 9.3 - Evaluate the following definite integrals:...Ch. 9.3 - Prob. 4ECh. 9.3 - Evaluate the following definite integrals:...Ch. 9.3 - Evaluate the following definite integrals:...Ch. 9.3 - Evaluate the following definite integrals:...Ch. 9.3 - Prob. 8ECh. 9.3 - Evaluate the following definite integrals:...Ch. 9.3 - Evaluate the following definite integrals:...Ch. 9.3 - Evaluate the following definite integrals:...Ch. 9.3 - Evaluate the following definite integrals:...Ch. 9.3 - Prob. 13ECh. 9.3 - Evaluate the following definite integrals:...Ch. 9.3 - Evaluate the following definite integrals:...Ch. 9.3 - Evaluate the following definite integrals: 1elnxdxCh. 9.3 - Prob. 17ECh. 9.3 - Prob. 18ECh. 9.3 - Prob. 19ECh. 9.3 - Prob. 20ECh. 9.3 - Prob. 21ECh. 9.3 - Prob. 22ECh. 9.3 - Prob. 23ECh. 9.3 - In Exercises 24 and 25, find the area of the...Ch. 9.3 - Prob. 25ECh. 9.4 - Consider 13.4(5x9)2dx. Divide the interval 1x3.4...Ch. 9.4 - Prob. 2CYUCh. 9.4 - Prob. 3CYUCh. 9.4 - Prob. 4CYUCh. 9.4 - Prob. 5CYUCh. 9.4 - Prob. 1ECh. 9.4 - Prob. 2ECh. 9.4 - Prob. 3ECh. 9.4 - Prob. 4ECh. 9.4 - Prob. 5ECh. 9.4 - Refer to the graph in Fig. 11. Apply the...Ch. 9.4 - Prob. 7ECh. 9.4 - Prob. 8ECh. 9.4 - Prob. 9ECh. 9.4 - Prob. 10ECh. 9.4 - Prob. 11ECh. 9.4 - Prob. 12ECh. 9.4 - Prob. 13ECh. 9.4 - Prob. 14ECh. 9.4 - Prob. 15ECh. 9.4 - Approximate the following integrals by the...Ch. 9.4 - Approximate the following integrals by the...Ch. 9.4 - Prob. 18ECh. 9.4 - Prob. 19ECh. 9.4 - Prob. 20ECh. 9.4 - Prob. 21ECh. 9.4 - Prob. 22ECh. 9.4 - The following integrals cannot be evaluated in...Ch. 9.4 - Prob. 24ECh. 9.4 - Prob. 25ECh. 9.4 - Area To determine the amount of water flowing down...Ch. 9.4 - Distance Traveled Upon takeoff, the velocity...Ch. 9.4 - Prob. 28ECh. 9.4 - Prob. 29ECh. 9.4 - Consider 12f(x)dx, where f(x)=3lnx. Make a rough...Ch. 9.4 - Prob. 31ECh. 9.4 - Prob. 32ECh. 9.4 - Prob. 33ECh. 9.4 - Prob. 34ECh. 9.4 - Prob. 35ECh. 9.4 - Prob. 36ECh. 9.4 - Technology Exercises In Exercises 3740,...Ch. 9.4 - Prob. 38ECh. 9.4 - Prob. 39ECh. 9.4 - Prob. 40ECh. 9.4 - Prob. 41ECh. 9.4 - Prob. 42ECh. 9.5 - The integral formula is used in many applications...Ch. 9.5 - Prob. 1ECh. 9.5 - Present valueA continuous stream of income is...Ch. 9.5 - Present valueFind the present value of a...Ch. 9.5 - Prob. 4ECh. 9.5 - Present value Find the present value of a...Ch. 9.5 - Present valueA continuous stream of income is...Ch. 9.5 - Prob. 7ECh. 9.5 - Prob. 8ECh. 9.5 - Prob. 9ECh. 9.5 - Prob. 10ECh. 9.5 - Prob. 11ECh. 9.5 - Prob. 12ECh. 9.5 - Prob. 13ECh. 9.6 - Prob. 1CYUCh. 9.6 - Prob. 2CYUCh. 9.6 - Prob. 3CYUCh. 9.6 - In Exercises 1-12, determine if the given...Ch. 9.6 - Prob. 2ECh. 9.6 - Prob. 3ECh. 9.6 - Prob. 4ECh. 9.6 - Prob. 5ECh. 9.6 - Prob. 6ECh. 9.6 - Prob. 7ECh. 9.6 - Prob. 8ECh. 9.6 - Prob. 9ECh. 9.6 - In Exercises 1-12, determine if the given...Ch. 9.6 - Prob. 11ECh. 9.6 - Prob. 12ECh. 9.6 - Find the area under the graph of y=1x2forx2.Ch. 9.6 - Prob. 14ECh. 9.6 - Find the area under the graph of y=ex/2forx0.Ch. 9.6 - Prob. 16ECh. 9.6 - Prob. 17ECh. 9.6 - Prob. 18ECh. 9.6 - Prob. 19ECh. 9.6 - Prob. 20ECh. 9.6 - Evaluate the following improper integrals whenever...Ch. 9.6 - Prob. 22ECh. 9.6 - Evaluate the following improper integrals whenever...Ch. 9.6 - Prob. 24ECh. 9.6 - Evaluate the following improper integrals whenever...Ch. 9.6 - Prob. 26ECh. 9.6 - Prob. 27ECh. 9.6 - Prob. 28ECh. 9.6 - Evaluate the following improper integrals whenever...Ch. 9.6 - Prob. 30ECh. 9.6 - Evaluate the following improper integrals whenever...Ch. 9.6 - Prob. 32ECh. 9.6 - Evaluate the following improper integrals whenever...Ch. 9.6 - Prob. 34ECh. 9.6 - Prob. 35ECh. 9.6 - Prob. 36ECh. 9.6 - Prob. 37ECh. 9.6 - Prob. 38ECh. 9.6 - Evaluate the following improper integrals whenever...Ch. 9.6 - Prob. 40ECh. 9.6 - Prob. 41ECh. 9.6 - Prob. 42ECh. 9.6 - Prob. 43ECh. 9.6 - Prob. 44ECh. 9.6 - Prob. 45ECh. 9.6 - Prob. 46ECh. 9.6 - Prob. 47ECh. 9.6 - Prob. 48ECh. 9.6 - Prob. 49ECh. 9.6 - Prob. 50ECh. 9 - Describe integration by substitution in your own...Ch. 9 - Prob. 2FCCECh. 9 - Prob. 3FCCECh. 9 - Prob. 4FCCECh. 9 - Prob. 5FCCECh. 9 - Prob. 6FCCECh. 9 - Prob. 7FCCECh. 9 - Prob. 8FCCECh. 9 - Prob. 9FCCECh. 9 - Prob. 10FCCECh. 9 - Determine the following indefinite integral:...Ch. 9 - Determine the following indefinite integral:...Ch. 9 - Determine the following indefinite integral:...Ch. 9 - Determine the following indefinite integral:...Ch. 9 - Determine the following indefinite integral:...Ch. 9 - Determine the following indefinite integral:...Ch. 9 - Determine the following indefinite integral:...Ch. 9 - Determine the following indefinite integral:...Ch. 9 - Determine the following indefinite integral:...Ch. 9 - Prob. 10RECh. 9 - Prob. 11RECh. 9 - Prob. 12RECh. 9 - Prob. 13RECh. 9 - Prob. 14RECh. 9 - Prob. 15RECh. 9 - Prob. 16RECh. 9 - Prob. 17RECh. 9 - Determine the following indefinite integral:...Ch. 9 - Prob. 19RECh. 9 - Prob. 20RECh. 9 - Prob. 21RECh. 9 - Prob. 22RECh. 9 - Prob. 23RECh. 9 - Prob. 24RECh. 9 - Prob. 25RECh. 9 - Prob. 26RECh. 9 - Prob. 27RECh. 9 - Prob. 28RECh. 9 - Prob. 29RECh. 9 - Prob. 30RECh. 9 - Prob. 31RECh. 9 - Prob. 32RECh. 9 - Prob. 33RECh. 9 - Prob. 34RECh. 9 - Prob. 35RECh. 9 - Prob. 36RECh. 9 - Evaluate the following definite integrals:...Ch. 9 - Prob. 38RECh. 9 - Prob. 39RECh. 9 - Prob. 40RECh. 9 - Prob. 41RECh. 9 - Prob. 42RECh. 9 - Prob. 43RECh. 9 - Prob. 44RECh. 9 - Prob. 45RECh. 9 - Prob. 46RECh. 9 - Evaluate the following improper integrals whenever...Ch. 9 - Prob. 48RECh. 9 - Prob. 49RECh. 9 - Prob. 50RECh. 9 - Prob. 51RECh. 9 - Prob. 52RECh. 9 - Prob. 53RECh. 9 - Prob. 54RECh. 9 - Prob. 55RECh. 9 - Prob. 56RECh. 9 - Prob. 57RECh. 9 - Prob. 58RE
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