Precalculus - Mathematics for Calculus - Seventh Edition
7th Edition
ISBN: 9781305750463
Author: Stewart
Publisher: CENGAGE C
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Chapter 8, Problem 30RE
30. −10i
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(7) (12 points) Let F(x, y, z) = (y, x+z cos yz, y cos yz).
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(a) (4 points) Show that V x F = 0.
(b) (4 points) Find a potential f for the vector field F.
(c) (4 points) Let S be a surface in R3 for which the Stokes' Theorem is valid. Use
Stokes' Theorem to calculate the line integral
Jos
F.ds;
as denotes the boundary of S. Explain your answer.
(3) (16 points) Consider
z = uv,
u = x+y,
v=x-y.
(a) (4 points) Express z in the form z = fog where g: R² R² and f: R² →
R.
(b) (4 points) Use the chain rule to calculate Vz = (2, 2). Show all intermediate
steps otherwise no credit.
(c) (4 points) Let S be the surface parametrized by
T(x, y) = (x, y, ƒ (g(x, y))
(x, y) = R².
Give a parametric description of the tangent plane to S at the point p = T(x, y).
(d) (4 points) Calculate the second Taylor polynomial Q(x, y) (i.e. the quadratic
approximation) of F = (fog) at a point (a, b). Verify that
Q(x,y) F(a+x,b+y).
=
(6) (8 points) Change the order of integration and evaluate
(z +4ry)drdy .
So S√ ²
0
Chapter 8 Solutions
Precalculus - Mathematics for Calculus - Seventh Edition
Ch. 8.1 - We can describe the location of a point in the...Ch. 8.1 - Prob. 2ECh. 8.1 - Yes or No? If No, give a reason. 3. Do the polar...Ch. 8.1 - Yes or No? If No, give a reason. 4. Do the...Ch. 8.1 - Prob. 5ECh. 8.1 - Prob. 6ECh. 8.1 - Prob. 7ECh. 8.1 - Prob. 8ECh. 8.1 - Prob. 9ECh. 8.1 - Prob. 10E
Ch. 8.1 - Prob. 11ECh. 8.1 - Prob. 12ECh. 8.1 - Prob. 13ECh. 8.1 - Prob. 14ECh. 8.1 - Prob. 15ECh. 8.1 - Prob. 16ECh. 8.1 - Points in Polar Coordinates Determine which point...Ch. 8.1 - Prob. 18ECh. 8.1 - Prob. 19ECh. 8.1 - Points in Polar Coordinates Determine which point...Ch. 8.1 - Prob. 21ECh. 8.1 - Prob. 22ECh. 8.1 - Points in Polar Coordinates Determine which point...Ch. 8.1 - Prob. 24ECh. 8.1 - Prob. 25ECh. 8.1 - Prob. 26ECh. 8.1 - Prob. 27ECh. 8.1 - Polar Coordinates to Rectangular Coordinates A...Ch. 8.1 - Prob. 29ECh. 8.1 - Prob. 30ECh. 8.1 - Prob. 31ECh. 8.1 - Prob. 32ECh. 8.1 - Prob. 33ECh. 8.1 - Prob. 34ECh. 8.1 - Prob. 35ECh. 8.1 - Prob. 36ECh. 8.1 - Prob. 37ECh. 8.1 - Prob. 38ECh. 8.1 - Prob. 39ECh. 8.1 - Prob. 40ECh. 8.1 - Prob. 41ECh. 8.1 - Prob. 42ECh. 8.1 - Prob. 43ECh. 8.1 - Prob. 44ECh. 8.1 - Prob. 45ECh. 8.1 - Prob. 46ECh. 8.1 - Prob. 47ECh. 8.1 - Prob. 48ECh. 8.1 - Prob. 49ECh. 8.1 - Prob. 50ECh. 8.1 - Prob. 51ECh. 8.1 - Prob. 52ECh. 8.1 - Prob. 53ECh. 8.1 - Prob. 54ECh. 8.1 - Prob. 55ECh. 8.1 - Prob. 56ECh. 8.1 - Prob. 57ECh. 8.1 - Prob. 58ECh. 8.1 - Prob. 59ECh. 8.1 - Prob. 60ECh. 8.1 - Prob. 61ECh. 8.1 - Prob. 62ECh. 8.1 - Prob. 63ECh. 8.1 - Prob. 64ECh. 8.1 - Prob. 65ECh. 8.1 - Prob. 66ECh. 8.1 - Prob. 67ECh. 8.1 - Prob. 68ECh. 8.1 - Prob. 69ECh. 8.1 - Prob. 70ECh. 8.1 - Prob. 71ECh. 8.1 - Prob. 72ECh. 8.2 - To plot points in polar coordinates, we use a grid...Ch. 8.2 - Prob. 2ECh. 8.2 - Prob. 3ECh. 8.2 - Prob. 4ECh. 8.2 - Prob. 5ECh. 8.2 - Prob. 6ECh. 8.2 - Prob. 7ECh. 8.2 - Prob. 8ECh. 8.2 - Prob. 9ECh. 8.2 - Prob. 10ECh. 8.2 - Prob. 11ECh. 8.2 - Prob. 12ECh. 8.2 - Prob. 13ECh. 8.2 - Prob. 14ECh. 8.2 - Prob. 15ECh. 8.2 - Prob. 16ECh. 8.2 - Prob. 17ECh. 8.2 - Prob. 18ECh. 8.2 - Prob. 19ECh. 8.2 - Prob. 20ECh. 8.2 - Prob. 21ECh. 8.2 - Prob. 22ECh. 8.2 - Prob. 23ECh. 8.2 - Prob. 24ECh. 8.2 - Prob. 25ECh. 8.2 - Prob. 26ECh. 8.2 - Prob. 27ECh. 8.2 - Prob. 28ECh. 8.2 - Prob. 29ECh. 8.2 - Prob. 30ECh. 8.2 - Prob. 31ECh. 8.2 - Prob. 32ECh. 8.2 - Prob. 33ECh. 8.2 - Prob. 34ECh. 8.2 - Prob. 35ECh. 8.2 - Prob. 36ECh. 8.2 - Prob. 37ECh. 8.2 - Prob. 38ECh. 8.2 - Prob. 39ECh. 8.2 - Prob. 40ECh. 8.2 - Prob. 41ECh. 8.2 - Prob. 42ECh. 8.2 - Prob. 43ECh. 8.2 - Prob. 44ECh. 8.2 - Prob. 45ECh. 8.2 - Prob. 46ECh. 8.2 - Prob. 47ECh. 8.2 - Prob. 48ECh. 8.2 - Prob. 49ECh. 8.2 - Prob. 50ECh. 8.2 - Prob. 51ECh. 8.2 - Prob. 52ECh. 8.2 - Prob. 53ECh. 8.2 - Prob. 54ECh. 8.2 - Prob. 55ECh. 8.2 - Prob. 56ECh. 8.2 - Prob. 57ECh. 8.2 - Prob. 58ECh. 8.2 - Rectangular to Polar Sketch a graph of the...Ch. 8.2 - Prob. 60ECh. 8.2 - Prob. 61ECh. 8.2 - Prob. 62ECh. 8.2 - Orbit of a Satellite Scientists and engineers...Ch. 8.2 - Prob. 64ECh. 8.2 - Prob. 65ECh. 8.2 - Prob. 66ECh. 8.2 - Prob. 67ECh. 8.3 - A complex number z = a + bi has two parts: a is...Ch. 8.3 - Let z = a + bi. (a) The modulus of z is r =...Ch. 8.3 - (a) The complex number z = 1 + i in polar form is...Ch. 8.3 - How many different nth roots does a nonzero...Ch. 8.3 - A Complex Number and Its Modulus Graph the complex...Ch. 8.3 - A Complex Number and Its Modulus Graph the complex...Ch. 8.3 - A Complex Number and Its Modulus Graph the complex...Ch. 8.3 - A Complex Number and Its Modulus Graph the complex...Ch. 8.3 - A Complex Number and Its Modulus Graph the complex...Ch. 8.3 - A Complex Number and Its Modulus Graph the complex...Ch. 8.3 - A Complex Number and Its Modulus Graph the complex...Ch. 8.3 - A Complex Number and Its Modulus Graph the complex...Ch. 8.3 - Prob. 13ECh. 8.3 - Prob. 14ECh. 8.3 - Prob. 15ECh. 8.3 - Prob. 16ECh. 8.3 - Graphing a Complex Number and Its Complex...Ch. 8.3 - Prob. 18ECh. 8.3 - Prob. 19ECh. 8.3 - Prob. 20ECh. 8.3 - Graphing Sets of Complex Numbers Sketch the set in...Ch. 8.3 - Prob. 22ECh. 8.3 - Prob. 23ECh. 8.3 - Graphing Sets of Complex Numbers Sketch the set in...Ch. 8.3 - Prob. 25ECh. 8.3 - Prob. 26ECh. 8.3 - Prob. 27ECh. 8.3 - Prob. 28ECh. 8.3 - Prob. 29ECh. 8.3 - Prob. 30ECh. 8.3 - Prob. 31ECh. 8.3 - Prob. 32ECh. 8.3 - Prob. 33ECh. 8.3 - Prob. 34ECh. 8.3 - Prob. 35ECh. 8.3 - Prob. 36ECh. 8.3 - Prob. 37ECh. 8.3 - Prob. 38ECh. 8.3 - Prob. 39ECh. 8.3 - Polar Form of Complex Numbers Write the complex...Ch. 8.3 - Prob. 41ECh. 8.3 - Prob. 42ECh. 8.3 - Prob. 43ECh. 8.3 - Polar Form of Complex Numbers Write the complex...Ch. 8.3 - Prob. 45ECh. 8.3 - Prob. 46ECh. 8.3 - Prob. 47ECh. 8.3 - Prob. 48ECh. 8.3 - Prob. 49ECh. 8.3 - Prob. 50ECh. 8.3 - Prob. 51ECh. 8.3 - Prob. 52ECh. 8.3 - Prob. 53ECh. 8.3 - Prob. 54ECh. 8.3 - Prob. 55ECh. 8.3 - Prob. 56ECh. 8.3 - Prob. 57ECh. 8.3 - Prob. 58ECh. 8.3 - Prob. 59ECh. 8.3 - Prob. 60ECh. 8.3 - Prob. 61ECh. 8.3 - Prob. 62ECh. 8.3 - Prob. 63ECh. 8.3 - Prob. 64ECh. 8.3 - Prob. 65ECh. 8.3 - Prob. 66ECh. 8.3 - Prob. 67ECh. 8.3 - Prob. 68ECh. 8.3 - Prob. 69ECh. 8.3 - Prob. 70ECh. 8.3 - Prob. 71ECh. 8.3 - Prob. 72ECh. 8.3 - Prob. 73ECh. 8.3 - Prob. 74ECh. 8.3 - Prob. 75ECh. 8.3 - Prob. 76ECh. 8.3 - Prob. 77ECh. 8.3 - Roots of Complex Numbers Find the indicated roots,...Ch. 8.3 - Prob. 79ECh. 8.3 - Prob. 80ECh. 8.3 - Prob. 81ECh. 8.3 - Prob. 82ECh. 8.3 - Prob. 83ECh. 8.3 - Prob. 84ECh. 8.3 - Prob. 85ECh. 8.3 - Prob. 86ECh. 8.3 - Prob. 87ECh. 8.3 - Prob. 88ECh. 8.3 - Prob. 89ECh. 8.3 - Prob. 90ECh. 8.3 - Prob. 91ECh. 8.3 - Prob. 92ECh. 8.3 - Prob. 93ECh. 8.3 - Prob. 94ECh. 8.3 - Prob. 95ECh. 8.3 - Prob. 96ECh. 8.3 - Prob. 97ECh. 8.3 - Prob. 98ECh. 8.3 - Prob. 99ECh. 8.3 - Prob. 100ECh. 8.3 - Prob. 101ECh. 8.4 - (a) The parametric equations x = f(t) and y = g(t)...Ch. 8.4 - (a) True or False? The same curve can be described...Ch. 8.4 - Prob. 3ECh. 8.4 - Prob. 4ECh. 8.4 - Prob. 5ECh. 8.4 - Prob. 6ECh. 8.4 - Prob. 7ECh. 8.4 - Prob. 8ECh. 8.4 - Prob. 9ECh. 8.4 - Prob. 10ECh. 8.4 - Prob. 11ECh. 8.4 - Prob. 12ECh. 8.4 - Sketching a Curve by Eliminating the Parameter A...Ch. 8.4 - Prob. 14ECh. 8.4 - Sketching a Curve by Eliminating the Parameter A...Ch. 8.4 - Sketching a Curve by Eliminating the Parameter A...Ch. 8.4 - Prob. 17ECh. 8.4 - Sketching a Curve by Eliminating the Parameter A...Ch. 8.4 - Prob. 19ECh. 8.4 - Sketching a Curve by Eliminating the Parameter A...Ch. 8.4 - Sketching a Curve by Eliminating the Parameter A...Ch. 8.4 - Prob. 22ECh. 8.4 - Prob. 23ECh. 8.4 - Prob. 24ECh. 8.4 - Prob. 25ECh. 8.4 - Sketching a Curve by Eliminating the Parameter A...Ch. 8.4 - Prob. 27ECh. 8.4 - Circular Motion The position of an object in...Ch. 8.4 - Prob. 29ECh. 8.4 - Prob. 30ECh. 8.4 - Parametric Equations for Curves Find parametric...Ch. 8.4 - Parametric Equations for Curves Find parametric...Ch. 8.4 - Prob. 33ECh. 8.4 - Parametric Equations for Curves Find parametric...Ch. 8.4 - Parametric Equations for Curves Find parametric...Ch. 8.4 - Parametric Equations for Curves Find parametric...Ch. 8.4 - Prob. 37ECh. 8.4 - Path of a Projectile Referring to Exercise 37,...Ch. 8.4 - Prob. 39ECh. 8.4 - Prob. 40ECh. 8.4 - Prob. 41ECh. 8.4 - Prob. 42ECh. 8.4 - Prob. 43ECh. 8.4 - Prob. 44ECh. 8.4 - Prob. 45ECh. 8.4 - Prob. 46ECh. 8.4 - Prob. 47ECh. 8.4 - Prob. 48ECh. 8.4 - Prob. 49ECh. 8.4 - Prob. 50ECh. 8.4 - Prob. 51ECh. 8.4 - Prob. 52ECh. 8.4 - Prob. 53ECh. 8.4 - Prob. 54ECh. 8.4 - Prob. 55ECh. 8.4 - Prolate Cycloid (a) In Exercise 55 if the point P...Ch. 8.4 - Parametric Equations of a Hyperbola Eliminate the...Ch. 8.4 - Prob. 58ECh. 8.4 - Prob. 59ECh. 8.4 - Prob. 60ECh. 8.4 - Prob. 61ECh. 8.4 - Prob. 62ECh. 8.4 - Hypocycloid A circle C of radius b rolls on the...Ch. 8.4 - Prob. 64ECh. 8.4 - Longbow Curve In the following figure, the circle...Ch. 8.4 - Prob. 66ECh. 8.4 - Eliminating the Parameter Eliminate the parameter ...Ch. 8.4 - The Rotary Engine The Mazda RX-8 uses an...Ch. 8.4 - Prob. 69ECh. 8.4 - DISCOVER WRITE: More Information in Parametric...Ch. 8.4 - Prob. 71ECh. 8 - (a) Explain the polar coordinate system. (b) Graph...Ch. 8 - Prob. 2RCCCh. 8 - Prob. 3RCCCh. 8 - Prob. 4RCCCh. 8 - Prob. 5RCCCh. 8 - Prob. 6RCCCh. 8 - Prob. 7RCCCh. 8 - Prob. 8RCCCh. 8 - Prob. 9RCCCh. 8 - Prob. 1RECh. 8 - Prob. 2RECh. 8 - Prob. 3RECh. 8 - Prob. 4RECh. 8 - Prob. 5RECh. 8 - Prob. 6RECh. 8 - Prob. 7RECh. 8 - Prob. 8RECh. 8 - Prob. 9RECh. 8 - Prob. 10RECh. 8 - Prob. 11RECh. 8 - Prob. 12RECh. 8 - Prob. 13RECh. 8 - Rectangular Equations to Polar Equations (a)...Ch. 8 - Prob. 15RECh. 8 - Prob. 16RECh. 8 - Polar Equations to Rectangular Equations (a)...Ch. 8 - Prob. 18RECh. 8 - Prob. 19RECh. 8 - Prob. 20RECh. 8 - Prob. 21RECh. 8 - Prob. 22RECh. 8 - Prob. 23RECh. 8 - Prob. 24RECh. 8 - Prob. 25RECh. 8 - Prob. 26RECh. 8 - Prob. 27RECh. 8 - Prob. 28RECh. 8 - Prob. 29RECh. 8 - Complex Numbers A complex number is given. (a)...Ch. 8 - Prob. 31RECh. 8 - Prob. 32RECh. 8 - Prob. 33RECh. 8 - Prob. 34RECh. 8 - Prob. 35RECh. 8 - Powers Using De Moivres Theorem Use De Moivres...Ch. 8 - Prob. 37RECh. 8 - Prob. 38RECh. 8 - Prob. 39RECh. 8 - Roots of Complex Numbers Find the indicated roots....Ch. 8 - Prob. 41RECh. 8 - Prob. 42RECh. 8 - Parametric Curves A pair of parametric equations...Ch. 8 - Prob. 44RECh. 8 - Prob. 45RECh. 8 - Prob. 46RECh. 8 - Prob. 47RECh. 8 - Prob. 48RECh. 8 - Finding Parametric Equations for a Curve In the...Ch. 8 - Prob. 1TCh. 8 - Prob. 2TCh. 8 - Prob. 3TCh. 8 - Prob. 4TCh. 8 - Prob. 5TCh. 8 - Prob. 6TCh. 8 - (a) Sketch the curve represented by the parametric...Ch. 8 - Find parametric equations for the line of slope 2...Ch. 8 - The position of an object in circular motion is...Ch. 8 - Prob. 1PCh. 8 - Path of a Baseball Suppose a baseball is thrown at...Ch. 8 - Path of a Rocket Suppose that a rocket is fired at...Ch. 8 - Firing a Missile The initial speed of a missile is...Ch. 8 - Prob. 5PCh. 8 - Shooting into the Wind Suppose that a projectile...Ch. 8 - Prob. 7P
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