Essential Calculus
2nd Edition
ISBN: 9781133490975
Author: Stewart, James
Publisher: Cengage Learning
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Chapter 9.1, Problem 4E
To determine
To plot: The curve using the parametric equations
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Use Laplace transform to solve the initial value problem
y' + y = tsin(t), y(0) = 0
The function g is defined by
g(x) = sec² x + tan x. What are all
solutions to g(x) = 1 on the interval
0 ≤ x ≤ 2π ?
A
x =
= 0, x
==
= 3,
x = π,
x =
7
4
,
4
and x 2π only
=
B
x =
4'
1, x = 1, x = 57
and x = 3 only
C
x =
πk and x =
- +πk
D
,
where is any integer
П
x = +πk and
П
x =
+πk, where k is
any integer
Vector v = PQ has initial point P (2, 14) and terminal point Q (7, 3). Vector v = RS has initial point R (29, 8) and terminal point S (12, 17).
Part A: Write u and v in linear form. Show all necessary work.
Part B: Write u and v in trigonometric form. Show all necessary work.
Part C: Find 7u − 4v. Show all necessary calculations.
Chapter 9 Solutions
Essential Calculus
Ch. 9.1 - 14 Sketch the curve by using the parametric...Ch. 9.1 - Prob. 2ECh. 9.1 - Prob. 3ECh. 9.1 - Prob. 4ECh. 9.1 - Prob. 5ECh. 9.1 - Prob. 6ECh. 9.1 - Prob. 7ECh. 9.1 - Prob. 8ECh. 9.1 - (a) Eliminate the parameter to find a Cartesian...Ch. 9.1 - (a) Eliminate the parameter to find a Cartesian...
Ch. 9.1 - (a) Eliminate the parameter to find a Cartesian...Ch. 9.1 - (a) Eliminate the parameter to find a Cartesian...Ch. 9.1 - Prob. 13ECh. 9.1 - Prob. 14ECh. 9.1 - 15-18 Describe the motion of a particle with...Ch. 9.1 - 15-18 Describe the motion of a particle with...Ch. 9.1 - Describe the motion of a particle with position...Ch. 9.1 - Describe the motion of a particle with position...Ch. 9.1 - Prob. 19ECh. 9.1 - Prob. 20ECh. 9.1 - Prob. 21ECh. 9.1 - Match the parametric equations with the graphs...Ch. 9.1 - Graph the curve x = y 2 sin y.Ch. 9.1 - Graph the curves y = x3 4x and x = y3 4y and...Ch. 9.1 - (a) Show that the parametric equations x = x1 +...Ch. 9.1 - Use a graphing device and the result of Exercise...Ch. 9.1 - Find parametric equations for the path of a...Ch. 9.1 - (a) Find parametric equations for the ellipse...Ch. 9.1 - Use a graphing calculator or computer to reproduce...Ch. 9.1 - Use a graphing calculator or computer to reproduce...Ch. 9.1 - Compare the curves represented by the parametric...Ch. 9.1 - Prob. 32ECh. 9.1 - Derive Equations 1 for the case /2Ch. 9.1 - Let P be a point at a distance d from the center...Ch. 9.1 - If a and b are fixed numbers, find parametric...Ch. 9.1 - A curve, called a witch of Maria Agnesi, consists...Ch. 9.1 - Prob. 37ECh. 9.1 - Prob. 38ECh. 9.1 - Investigate the family of curves defined by the...Ch. 9.1 - The swallowtail catastrophe curves are defined by...Ch. 9.1 - Graph several members of the family of curves with...Ch. 9.1 - Graph several members of the family of curves x =...Ch. 9.1 - The curves with x = a sin nt, y = b cos t, called...Ch. 9.1 - Prob. 44ECh. 9.2 - Find dy/dx. x = t sin t, y = t2 + tCh. 9.2 - Find dy/dx. x = 1/t, y=tetCh. 9.2 - Find an equation of the tangent to the curve at...Ch. 9.2 - Find an equation of the tangent to the curve at...Ch. 9.2 - Find an equation of the tangent to the curve at...Ch. 9.2 - Find an equation of the tangent to the curve at...Ch. 9.2 - Find an equation of the tangent to the curve at...Ch. 9.2 - Find equations of the tangents to the curve x =...Ch. 9.2 - Find dy/dx and d2y/dx2. For which values of t is...Ch. 9.2 - Find dy/dx and d2y/dx2. For which values of t is...Ch. 9.2 - Find dy/dx and d2y/dx2. For which values of t is...Ch. 9.2 - 912 Find dy/dx and d2y/dx2. For which values t of...Ch. 9.2 - Prob. 13ECh. 9.2 - Prob. 14ECh. 9.2 - Find the points on the curve where the tangent is...Ch. 9.2 - Find the points on the curve where the tangent is...Ch. 9.2 - Prob. 17ECh. 9.2 - Prob. 18ECh. 9.2 - Prob. 19ECh. 9.2 - Prob. 20ECh. 9.2 - Show that the curve x = cos t, y = sin t cos t has...Ch. 9.2 - Graph the curve x = cos t + 2 cos 2t, y = sin t +...Ch. 9.2 - Prob. 23ECh. 9.2 - Prob. 24ECh. 9.2 - At what points on the curve x = 2t3, y = 1 + 4t ...Ch. 9.2 - Prob. 26ECh. 9.2 - Prob. 27ECh. 9.2 - Find the area enclosed by the curve x = t2 2t,...Ch. 9.2 - Find the area enclosed by the x-axis and the curve...Ch. 9.2 - Prob. 30ECh. 9.2 - Prob. 31ECh. 9.2 - Prob. 32ECh. 9.2 - Prob. 33ECh. 9.2 - Prob. 34ECh. 9.2 - Prob. 35ECh. 9.2 - Prob. 36ECh. 9.2 - Prob. 37ECh. 9.2 - Prob. 38ECh. 9.2 - Prob. 39ECh. 9.2 - Prob. 40ECh. 9.2 - Prob. 41ECh. 9.2 - Prob. 42ECh. 9.2 - Prob. 43ECh. 9.2 - Find the length of the loop of the curve x = 3t ...Ch. 9.2 - Prob. 45ECh. 9.2 - Prob. 46ECh. 9.2 - Prob. 47ECh. 9.2 - Prob. 48ECh. 9.2 - Prob. 49ECh. 9.2 - Prob. 50ECh. 9.2 - Prob. 51ECh. 9.2 - A string is wound around a circle and then unwound...Ch. 9.2 - A cow is tied to a silo with radius r by a rope...Ch. 9.3 - Prob. 1ECh. 9.3 - Prob. 2ECh. 9.3 - Prob. 3ECh. 9.3 - Prob. 4ECh. 9.3 - Prob. 5ECh. 9.3 - Prob. 6ECh. 9.3 - Prob. 7ECh. 9.3 - Prob. 8ECh. 9.3 - Prob. 9ECh. 9.3 - Prob. 10ECh. 9.3 - Prob. 11ECh. 9.3 - Prob. 12ECh. 9.3 - Identify the curve by finding a Cartesian equation...Ch. 9.3 - Identify the curve by finding a Cartesian equation...Ch. 9.3 - Identify the curve by finding a Cartesian equation...Ch. 9.3 - Prob. 16ECh. 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 - Sketch the curve with the given polar equation by...Ch. 9.3 - Sketch the curve with the given polar equation by...Ch. 9.3 - Sketch the curve with the given polar equation by...Ch. 9.3 - Sketch the curve with the given polar equation by...Ch. 9.3 - Sketch the curve with the given polar equation by...Ch. 9.3 - 2340 Sketch the curve with the given polar...Ch. 9.3 - 2340 Sketch the curve with the given polar...Ch. 9.3 - Prob. 30ECh. 9.3 - Sketch the curve with the given polar equation by...Ch. 9.3 - Sketch the curve with the given polar equation by...Ch. 9.3 - 2340 Sketch the curve with the given polar...Ch. 9.3 - Prob. 34ECh. 9.3 - Prob. 35ECh. 9.3 - Sketch the curve with the given polar equation by...Ch. 9.3 - Sketch the curve with the given polar equation by...Ch. 9.3 - Prob. 38ECh. 9.3 - Prob. 39ECh. 9.3 - Prob. 40ECh. 9.3 - Prob. 41ECh. 9.3 - Prob. 42ECh. 9.3 - Prob. 43ECh. 9.3 - Prob. 45ECh. 9.3 - Prob. 44ECh. 9.3 - Prob. 46ECh. 9.3 - Prob. 47ECh. 9.3 - Find the slope of the tangent line to the given...Ch. 9.3 - Prob. 49ECh. 9.3 - Find the slope of the tangent line to the given...Ch. 9.3 - Prob. 51ECh. 9.3 - Prob. 54ECh. 9.3 - Prob. 53ECh. 9.3 - Find the points on the given curve where the...Ch. 9.3 - Prob. 55ECh. 9.3 - Prob. 56ECh. 9.3 - Prob. 57ECh. 9.3 - Prob. 60ECh. 9.3 - Prob. 59ECh. 9.3 - Prob. 58ECh. 9.3 - How are the graphs of r = 1 + sin( /6) and r = 1...Ch. 9.3 - Use a graph to estimate the y-coordinate of the...Ch. 9.3 - Prob. 63ECh. 9.3 - Prob. 64ECh. 9.3 - A family of curves has polar equations...Ch. 9.3 - Let P be any point (except the origin) on the...Ch. 9.3 - Prob. 68ECh. 9.4 - Find the area of the region that is bounded by the...Ch. 9.4 - Prob. 2ECh. 9.4 - Find the area of the region that is bounded by the...Ch. 9.4 - Prob. 4ECh. 9.4 - Prob. 6ECh. 9.4 - Prob. 8ECh. 9.4 - Find the area of the shaded region. 7.Ch. 9.4 - Find the area of the shaded region. 5.Ch. 9.4 - Sketch the curve and find the area that it...Ch. 9.4 - Sketch the curve and find the area that it...Ch. 9.4 - Prob. 11ECh. 9.4 - 912 Sketch the curve and find the area that it...Ch. 9.4 - Prob. 14ECh. 9.4 - Graph the curve and find the area that it...Ch. 9.4 - Find the area of the region enclosed by one loop...Ch. 9.4 - 1518 Find the area of the region enclosed by one...Ch. 9.4 - Prob. 17ECh. 9.4 - Prob. 18ECh. 9.4 - 19-22 Find the area of the region that lies inside...Ch. 9.4 - Find the area of the region that lies inside the...Ch. 9.4 - Find the area of the region that lies inside the...Ch. 9.4 - Prob. 22ECh. 9.4 - 2326 Find the area of the region that lies inside...Ch. 9.4 - Find the area of the region that lies inside both...Ch. 9.4 - Find the area of the region that lies inside both...Ch. 9.4 - Prob. 26ECh. 9.4 - Prob. 27ECh. 9.4 - Prob. 29ECh. 9.4 - Prob. 30ECh. 9.4 - Find all points of intersection of the given...Ch. 9.4 - Prob. 32ECh. 9.4 - When recording live performances, sound engineers...Ch. 9.4 - 3336 Find the exact length of the polar curve. 33....Ch. 9.4 - 3336 Find the exact length of the polar curve. 34....Ch. 9.4 - Find the exact length of the polar curve. 47. r =...Ch. 9.4 - Prob. 36ECh. 9.4 - Prob. 37ECh. 9.4 - Prob. 38ECh. 9.5 - Prob. 1ECh. 9.5 - Prob. 2ECh. 9.5 - Prob. 3ECh. 9.5 - Prob. 4ECh. 9.5 - Prob. 7ECh. 9.5 - Prob. 6ECh. 9.5 - Prob. 5ECh. 9.5 - Prob. 8ECh. 9.5 - Prob. 9ECh. 9.5 - Prob. 10ECh. 9.5 - Prob. 11ECh. 9.5 - Prob. 12ECh. 9.5 - Prob. 13ECh. 9.5 - Prob. 14ECh. 9.5 - Prob. 15ECh. 9.5 - Prob. 16ECh. 9.5 - Prob. 17ECh. 9.5 - Prob. 18ECh. 9.5 - Prob. 19ECh. 9.5 - Prob. 20ECh. 9.5 - Prob. 21ECh. 9.5 - Prob. 22ECh. 9.5 - Prob. 23ECh. 9.5 - Prob. 24ECh. 9.5 - The orbit of Halleys comet, last seen in 1986 and...Ch. 9.5 - Prob. 26ECh. 9.5 - Prob. 27ECh. 9.5 - The distance from the dwarf planet Pluto to the...Ch. 9.5 - Prob. 29ECh. 9 - Prob. 1RCCCh. 9 - Prob. 2RCCCh. 9 - Prob. 3RCCCh. 9 - Prob. 4RCCCh. 9 - Prob. 5RCCCh. 9 - Prob. 6RCCCh. 9 - Determine whether the statement is true or false....Ch. 9 - Prob. 2RQCh. 9 - Determine whether the statement is true or false....Ch. 9 - Prob. 4RQCh. 9 - Prob. 5RQCh. 9 - Prob. 6RQCh. 9 - Prob. 7RQCh. 9 - Prob. 8RQCh. 9 - Prob. 1RECh. 9 - Prob. 2RECh. 9 - Prob. 3RECh. 9 - Prob. 4RECh. 9 - Prob. 5RECh. 9 - Prob. 6RECh. 9 - Prob. 7RECh. 9 - Sketch the region consisting of points whose polar...Ch. 9 - Prob. 9RECh. 9 - Prob. 10RECh. 9 - Sketch the polar curve. 11. r = cos 3Ch. 9 - Sketch the polar curve. 12. r = 3 + cos 3Ch. 9 - Sketch the polar curve. 13. r = 1 + cos 2Ch. 9 - Sketch the polar curve. 14. r = 2 cos(/2)Ch. 9 - Sketch the polar curve. 15. r=31+2sinCh. 9 - Sketch the polar curve. 16. r=322cosCh. 9 - Find a polar equation for the curve represented by...Ch. 9 - Find a polar equation for the curve represented by...Ch. 9 - The curve with polar equation r = (sin )/ is...Ch. 9 - Prob. 20RECh. 9 - Find the slope of the tangent line to the given...Ch. 9 - Find the slope of the tangent line to the given...Ch. 9 - Find the slope of the tangent line to the given...Ch. 9 - Find the slope of the tangent line to the given...Ch. 9 - Find dy/dx and d2y/dx2. 25. x = t + sin t, y = t ...Ch. 9 - Prob. 26RECh. 9 - Prob. 27RECh. 9 - Prob. 28RECh. 9 - At what points does the curve x = 2a cos t a cos...Ch. 9 - Find the area enclosed by the curve in Exercise...Ch. 9 - Prob. 31RECh. 9 - Prob. 32RECh. 9 - Prob. 33RECh. 9 - Prob. 34RECh. 9 - Prob. 35RECh. 9 - Prob. 36RECh. 9 - Prob. 37RECh. 9 - Prob. 38RECh. 9 - Prob. 39RECh. 9 - Prob. 40RECh. 9 - The curves defined by the parametric equations...Ch. 9 - Prob. 42RECh. 9 - Prob. 43RECh. 9 - Prob. 44RECh. 9 - In the figure the circle of radius a is...
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