EBK SINGLE VARIABLE CALCULUS
8th Edition
ISBN: 8220101383693
Author: Stewart
Publisher: Cengage Learning US
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Textbook Question
Chapter 10.4, Problem 55E
- (a) Use Formula 10.2.6 to show that the area of the surface generated by rotating the polar curve
(where f′ is continuous and 0 ≤ a < b ≤ π) about the polar axis is
- (b) Use the formula in part (a) to find the surface area generated by rotating the lemniscate r2 = cos 2θ about the polar axis.
Expert Solution & Answer
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Use the information in the following table to find h' (a) at the given value for a.
x|f(x) g(x) f'(x) g(x)
0
0
0
4
3
1
4
4
3
0
2
7
1
2
7
3
3
1
2
9
4
0
4
5
7
h(x) = f(g(x)); a = 0
h' (0) =
Use the information in the following table to find h' (a) at the given value for a.
x f(x) g(x) f'(x) g'(x)
0
0
3
2
1
1
0
0
2
0
2
43
22
4
3
3
2
3
1
1
4
1
2
0
4
2
h(x) = (1/(2) ²;
9(x)
h' (3)=
=
; a=3
The position of a moving hockey puck after t seconds is s(t) = tan
a. Find the velocity of the hockey puck at any time t.
v(t)
=====
b. Find the acceleration of the puck at any time t.
-1
a (t)
=
(t) where s is in meters.
c. Evaluate v(t) and a (t) for t = 1, 4, and 5 seconds. Round to 4 decimal places, if necessary.
v (1)
v (4)
v (5)
a (1)
=
=
=
=
a (4) =
a (5) =
d. What conclusion can be drawn from the results in the previous part?
○ The hockey puck is decelerating/slowing down at 1, 4, and 5 seconds
○ The hockey puck has a constant velocity/speed at 1, 4, and 5 seconds
○ The hockey puck is accelerating/speeding up at 1, 4, and 5 seconds
Chapter 10 Solutions
EBK SINGLE VARIABLE CALCULUS
Ch. 10.1 - Sketch the curve by using the parametric equations...Ch. 10.1 - Sketch the curve by using the parametric equations...Ch. 10.1 - Prob. 3ECh. 10.1 - Prob. 4ECh. 10.1 - Prob. 5ECh. 10.1 - Prob. 6ECh. 10.1 - Prob. 7ECh. 10.1 - Prob. 8ECh. 10.1 - Prob. 9ECh. 10.1 - Prob. 10E
Ch. 10.1 - Prob. 11ECh. 10.1 - Prob. 12ECh. 10.1 - Prob. 13ECh. 10.1 - Prob. 14ECh. 10.1 - Prob. 15ECh. 10.1 - Prob. 16ECh. 10.1 - Prob. 17ECh. 10.1 - Prob. 18ECh. 10.1 - Prob. 19ECh. 10.1 - Prob. 20ECh. 10.1 - Describe the motion of a particle with position...Ch. 10.1 - Prob. 22ECh. 10.1 - Prob. 23ECh. 10.1 - Prob. 24ECh. 10.1 - Prob. 25ECh. 10.1 - Prob. 26ECh. 10.1 - Prob. 27ECh. 10.1 - Match the parametric equations with the graphs...Ch. 10.1 - Prob. 29ECh. 10.1 - Prob. 30ECh. 10.1 - Prob. 31ECh. 10.1 - Use a graphing device and the result of Exercise...Ch. 10.1 - Prob. 33ECh. 10.1 - Prob. 34ECh. 10.1 - Prob. 35ECh. 10.1 - Prob. 36ECh. 10.1 - Prob. 37ECh. 10.1 - Prob. 38ECh. 10.1 - Prob. 39ECh. 10.1 - Prob. 40ECh. 10.1 - Prob. 41ECh. 10.1 - Prob. 42ECh. 10.1 - Prob. 43ECh. 10.1 - (a) Find parametric equations for the set of all...Ch. 10.1 - Suppose that the position of one particle at time...Ch. 10.1 - Prob. 46ECh. 10.1 - Prob. 47ECh. 10.1 - Prob. 48ECh. 10.1 - Prob. 49ECh. 10.1 - Prob. 50ECh. 10.1 - Prob. 51ECh. 10.1 - Prob. 52ECh. 10.2 - Prob. 1ECh. 10.2 - Prob. 2ECh. 10.2 - Prob. 3ECh. 10.2 - Prob. 4ECh. 10.2 - Prob. 5ECh. 10.2 - Prob. 6ECh. 10.2 - Prob. 7ECh. 10.2 - Prob. 8ECh. 10.2 - Prob. 9ECh. 10.2 - Find an equation of the tangent to the curve at...Ch. 10.2 - Prob. 11ECh. 10.2 - Prob. 12ECh. 10.2 - Prob. 13ECh. 10.2 - Prob. 14ECh. 10.2 - Find dy/dx and d2y/dx2. For which values of t is...Ch. 10.2 - Prob. 16ECh. 10.2 - Prob. 17ECh. 10.2 - Prob. 18ECh. 10.2 - Prob. 19ECh. 10.2 - Prob. 20ECh. 10.2 - Use a graph to estimate the coordinates of the...Ch. 10.2 - Prob. 22ECh. 10.2 - Prob. 23ECh. 10.2 - Prob. 24ECh. 10.2 - Prob. 25ECh. 10.2 - Prob. 26ECh. 10.2 - (a) Find the slope of the tangent line to the...Ch. 10.2 - Prob. 28ECh. 10.2 - At what point(s) on the curve x = 3t2 + 1, y = t3 ...Ch. 10.2 - Prob. 30ECh. 10.2 - Use the parametric equations of an ellipse, x = a...Ch. 10.2 - Find the area enclosed by the curve x = t2 2t,...Ch. 10.2 - Prob. 33ECh. 10.2 - Prob. 34ECh. 10.2 - Prob. 35ECh. 10.2 - Prob. 36ECh. 10.2 - Prob. 37ECh. 10.2 - Prob. 38ECh. 10.2 - Prob. 39ECh. 10.2 - Prob. 40ECh. 10.2 - Find the exact length of the curve. 41. x = 1 +...Ch. 10.2 - Find the exact length of the curve. 42. x = et t,...Ch. 10.2 - Prob. 43ECh. 10.2 - Prob. 44ECh. 10.2 - Prob. 45ECh. 10.2 - Prob. 46ECh. 10.2 - Prob. 47ECh. 10.2 - Prob. 48ECh. 10.2 - Prob. 49ECh. 10.2 - In Exercise 10.1.43 you were asked to derive the...Ch. 10.2 - Prob. 51ECh. 10.2 - Prob. 52ECh. 10.2 - Prob. 53ECh. 10.2 - Prob. 54ECh. 10.2 - (a) Graph the epitrochoid with equations...Ch. 10.2 - Prob. 57ECh. 10.2 - Set up an integral that represents the area of the...Ch. 10.2 - Prob. 59ECh. 10.2 - Prob. 60ECh. 10.2 - Prob. 61ECh. 10.2 - Prob. 62ECh. 10.2 - Prob. 63ECh. 10.2 - Prob. 64ECh. 10.2 - Prob. 65ECh. 10.2 - Prob. 66ECh. 10.2 - Prob. 67ECh. 10.2 - Prob. 68ECh. 10.2 - Prob. 69ECh. 10.2 - (a) Use the formula in Exercise 69(b) to find the...Ch. 10.2 - Prob. 71ECh. 10.2 - Prob. 72ECh. 10.2 - A string is wound around a circle and then unwound...Ch. 10.2 - A cow is tied to a silo with radius r by a rope...Ch. 10.3 - Prob. 1ECh. 10.3 - Prob. 2ECh. 10.3 - Plot the point whose polar coordinates are given....Ch. 10.3 - Plot the point whose polar coordinates are given....Ch. 10.3 - The Cartesian coordinates of a point are given....Ch. 10.3 - Prob. 6ECh. 10.3 - Prob. 7ECh. 10.3 - Prob. 8ECh. 10.3 - Prob. 9ECh. 10.3 - Prob. 10ECh. 10.3 - Prob. 11ECh. 10.3 - Prob. 12ECh. 10.3 - Prob. 13ECh. 10.3 - Prob. 14ECh. 10.3 - Prob. 15ECh. 10.3 - Prob. 16ECh. 10.3 - Identify the curve by finding a Cartesian equation...Ch. 10.3 - Identify the curve by finding a Cartesian equation...Ch. 10.3 - Prob. 19ECh. 10.3 - Prob. 20ECh. 10.3 - Prob. 21ECh. 10.3 - Prob. 22ECh. 10.3 - Prob. 23ECh. 10.3 - Prob. 24ECh. 10.3 - Prob. 25ECh. 10.3 - Prob. 26ECh. 10.3 - Prob. 27ECh. 10.3 - Prob. 28ECh. 10.3 - Prob. 29ECh. 10.3 - Prob. 30ECh. 10.3 - Prob. 31ECh. 10.3 - Prob. 32ECh. 10.3 - Prob. 33ECh. 10.3 - Prob. 34ECh. 10.3 - Prob. 35ECh. 10.3 - Prob. 36ECh. 10.3 - Prob. 37ECh. 10.3 - Prob. 38ECh. 10.3 - Prob. 39ECh. 10.3 - Prob. 40ECh. 10.3 - Sketch the curve with the given polar equation by...Ch. 10.3 - Sketch the curve with the given polar equation by...Ch. 10.3 - Prob. 43ECh. 10.3 - Prob. 44ECh. 10.3 - Prob. 45ECh. 10.3 - Prob. 46ECh. 10.3 - Prob. 47ECh. 10.3 - Prob. 48ECh. 10.3 - Prob. 49ECh. 10.3 - Prob. 50ECh. 10.3 - Prob. 51ECh. 10.3 - Prob. 52ECh. 10.3 - Prob. 53ECh. 10.3 - Prob. 54ECh. 10.3 - Prob. 55ECh. 10.3 - Prob. 56ECh. 10.3 - Prob. 57ECh. 10.3 - Prob. 58ECh. 10.3 - Prob. 59ECh. 10.3 - Prob. 60ECh. 10.3 - Prob. 61ECh. 10.3 - Prob. 62ECh. 10.3 - Prob. 63ECh. 10.3 - Prob. 64ECh. 10.3 - Prob. 65ECh. 10.3 - Prob. 66ECh. 10.3 - Use a graphing device to graph the polar curve....Ch. 10.3 - Prob. 68ECh. 10.3 - Use a graphing device to graph the polar curve....Ch. 10.3 - Prob. 70ECh. 10.3 - Use a graphing device to graph the polar curve....Ch. 10.3 - Prob. 72ECh. 10.3 - Prob. 73ECh. 10.3 - Prob. 74ECh. 10.3 - Prob. 75ECh. 10.3 - Prob. 76ECh. 10.3 - Prob. 77ECh. 10.3 - Prob. 78ECh. 10.4 - Find the area of the region that is bounded by the...Ch. 10.4 - Prob. 2ECh. 10.4 - Prob. 3ECh. 10.4 - Prob. 4ECh. 10.4 - Find the area of the shaded region. 5.Ch. 10.4 - Prob. 6ECh. 10.4 - Prob. 7ECh. 10.4 - Prob. 8ECh. 10.4 - Prob. 9ECh. 10.4 - Prob. 10ECh. 10.4 - Prob. 11ECh. 10.4 - Prob. 12ECh. 10.4 - Prob. 13ECh. 10.4 - Prob. 14ECh. 10.4 - Prob. 15ECh. 10.4 - Prob. 16ECh. 10.4 - Prob. 17ECh. 10.4 - Prob. 18ECh. 10.4 - Prob. 19ECh. 10.4 - Prob. 20ECh. 10.4 - Prob. 21ECh. 10.4 - Prob. 22ECh. 10.4 - Prob. 23ECh. 10.4 - Prob. 24ECh. 10.4 - Find the area of the region that lies inside the...Ch. 10.4 - Prob. 26ECh. 10.4 - Prob. 27ECh. 10.4 - Prob. 28ECh. 10.4 - Prob. 29ECh. 10.4 - Prob. 30ECh. 10.4 - Prob. 31ECh. 10.4 - Prob. 32ECh. 10.4 - Prob. 33ECh. 10.4 - Prob. 34ECh. 10.4 - Prob. 35ECh. 10.4 - Prob. 36ECh. 10.4 - Prob. 37ECh. 10.4 - Prob. 38ECh. 10.4 - Prob. 39ECh. 10.4 - Prob. 40ECh. 10.4 - Prob. 41ECh. 10.4 - Prob. 42ECh. 10.4 - The points of intersection of the cardioid r = 1 +...Ch. 10.4 - When recording live performances, sound engineers...Ch. 10.4 - Prob. 45ECh. 10.4 - Find the exact length of the polar curve. 46. r =...Ch. 10.4 - Prob. 47ECh. 10.4 - Prob. 48ECh. 10.4 - Find the exact length of the curve. Use a graph to...Ch. 10.4 - Find the exact length of the curve. Use a graph to...Ch. 10.4 - Prob. 51ECh. 10.4 - Prob. 52ECh. 10.4 - Prob. 53ECh. 10.4 - Use a calculator to find the length of the curve...Ch. 10.4 - (a) Use Formula 10.2.6 to show that the area of...Ch. 10.4 - Prob. 56ECh. 10.5 - Prob. 1ECh. 10.5 - Prob. 2ECh. 10.5 - Prob. 3ECh. 10.5 - Prob. 4ECh. 10.5 - Prob. 5ECh. 10.5 - Prob. 6ECh. 10.5 - Prob. 7ECh. 10.5 - Prob. 8ECh. 10.5 - Prob. 9ECh. 10.5 - Prob. 10ECh. 10.5 - Prob. 11ECh. 10.5 - Prob. 12ECh. 10.5 - Prob. 13ECh. 10.5 - Prob. 14ECh. 10.5 - Prob. 15ECh. 10.5 - Prob. 16ECh. 10.5 - Prob. 17ECh. 10.5 - Prob. 18ECh. 10.5 - Prob. 19ECh. 10.5 - Prob. 20ECh. 10.5 - Prob. 21ECh. 10.5 - Prob. 22ECh. 10.5 - Prob. 23ECh. 10.5 - Prob. 24ECh. 10.5 - Prob. 25ECh. 10.5 - Prob. 26ECh. 10.5 - Prob. 27ECh. 10.5 - Prob. 28ECh. 10.5 - Prob. 29ECh. 10.5 - Prob. 30ECh. 10.5 - Prob. 31ECh. 10.5 - Prob. 32ECh. 10.5 - Prob. 33ECh. 10.5 - Prob. 34ECh. 10.5 - Prob. 35ECh. 10.5 - Prob. 36ECh. 10.5 - Prob. 37ECh. 10.5 - Prob. 38ECh. 10.5 - Prob. 39ECh. 10.5 - Prob. 40ECh. 10.5 - Prob. 41ECh. 10.5 - Prob. 42ECh. 10.5 - Prob. 43ECh. 10.5 - Prob. 44ECh. 10.5 - Prob. 45ECh. 10.5 - Prob. 46ECh. 10.5 - Prob. 47ECh. 10.5 - Prob. 48ECh. 10.5 - Prob. 49ECh. 10.5 - Prob. 50ECh. 10.5 - Prob. 51ECh. 10.5 - Prob. 52ECh. 10.5 - Show that the function defined by the upper branch...Ch. 10.5 - Prob. 54ECh. 10.5 - Determine the type of curve represented by the...Ch. 10.5 - Prob. 56ECh. 10.5 - Show that the tangent lines to the parabola x2 =...Ch. 10.5 - Show that if an ellipse and a hyperbola have the...Ch. 10.5 - Prob. 59ECh. 10.5 - Prob. 60ECh. 10.5 - Find the area of the region enclosed by the...Ch. 10.5 - Prob. 62ECh. 10.5 - Prob. 63ECh. 10.5 - (a) Calculate the surface area of the ellipsoid...Ch. 10.5 - Prob. 65ECh. 10.5 - Prob. 66ECh. 10.6 - Prob. 1ECh. 10.6 - Prob. 2ECh. 10.6 - Prob. 3ECh. 10.6 - Prob. 4ECh. 10.6 - Prob. 5ECh. 10.6 - Prob. 6ECh. 10.6 - Prob. 7ECh. 10.6 - Prob. 8ECh. 10.6 - Prob. 9ECh. 10.6 - Prob. 10ECh. 10.6 - Prob. 11ECh. 10.6 - Prob. 12ECh. 10.6 - Prob. 13ECh. 10.6 - Prob. 14ECh. 10.6 - Prob. 15ECh. 10.6 - Prob. 16ECh. 10.6 - Prob. 17ECh. 10.6 - Prob. 18ECh. 10.6 - Prob. 19ECh. 10.6 - Prob. 20ECh. 10.6 - Prob. 21ECh. 10.6 - Prob. 22ECh. 10.6 - Prob. 23ECh. 10.6 - Prob. 24ECh. 10.6 - Prob. 25ECh. 10.6 - Prob. 26ECh. 10.6 - The orbit of Halleys comet, last seen in 1986 and...Ch. 10.6 - Prob. 28ECh. 10.6 - The planet Mercury travels in an elliptical orbit...Ch. 10.6 - The distance from the dwarf planet Pluto to the...Ch. 10.6 - Prob. 31ECh. 10 - Prob. 1RCCCh. 10 - Prob. 2RCCCh. 10 - Prob. 3RCCCh. 10 - Prob. 4RCCCh. 10 - Prob. 5RCCCh. 10 - Prob. 6RCCCh. 10 - Prob. 7RCCCh. 10 - Prob. 8RCCCh. 10 - Prob. 9RCCCh. 10 - Prob. 1RQCh. 10 - Prob. 2RQCh. 10 - Prob. 3RQCh. 10 - Prob. 4RQCh. 10 - Determine whether the statement is true or false....Ch. 10 - Prob. 6RQCh. 10 - Prob. 7RQCh. 10 - Prob. 8RQCh. 10 - Prob. 9RQCh. 10 - Prob. 10RQCh. 10 - Prob. 1RECh. 10 - Prob. 2RECh. 10 - Prob. 3RECh. 10 - Prob. 4RECh. 10 - Prob. 5RECh. 10 - Prob. 6RECh. 10 - Prob. 7RECh. 10 - Prob. 8RECh. 10 - Prob. 9RECh. 10 - Prob. 10RECh. 10 - Prob. 11RECh. 10 - Prob. 12RECh. 10 - Prob. 13RECh. 10 - Sketch the polar curve. 14. r = 2 cos(/2)Ch. 10 - Prob. 15RECh. 10 - Prob. 16RECh. 10 - Prob. 17RECh. 10 - Prob. 18RECh. 10 - Prob. 19RECh. 10 - Prob. 20RECh. 10 - Prob. 21RECh. 10 - Prob. 22RECh. 10 - Prob. 23RECh. 10 - Prob. 24RECh. 10 - Prob. 25RECh. 10 - Prob. 26RECh. 10 - Prob. 27RECh. 10 - Prob. 28RECh. 10 - Prob. 29RECh. 10 - Prob. 30RECh. 10 - Prob. 31RECh. 10 - Prob. 32RECh. 10 - Find the points of intersection of the curves r =...Ch. 10 - Prob. 34RECh. 10 - Find the area of the region that lies inside both...Ch. 10 - Find the area of the region that lies inside the...Ch. 10 - Prob. 37RECh. 10 - Prob. 38RECh. 10 - Prob. 39RECh. 10 - Prob. 40RECh. 10 - Find the area of the surface obtained by rotating...Ch. 10 - Prob. 42RECh. 10 - Prob. 43RECh. 10 - Prob. 44RECh. 10 - Prob. 45RECh. 10 - Prob. 46RECh. 10 - Prob. 47RECh. 10 - Prob. 48RECh. 10 - Prob. 49RECh. 10 - Prob. 50RECh. 10 - Prob. 51RECh. 10 - Prob. 52RECh. 10 - Prob. 53RECh. 10 - Prob. 54RECh. 10 - Prob. 55RECh. 10 - Prob. 56RECh. 10 - Prob. 57RECh. 10 - A curve called the folium of Descartes is defined...Ch. 10 - Prob. 1PCh. 10 - Prob. 2PCh. 10 - What is the smallest viewing rectangle that...Ch. 10 - Four bugs are placed at the four comers of a...Ch. 10 - Prob. 5PCh. 10 - A circle C of radius 2r has its center at the...
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