 21.1.1: In Exercises 14 decide if the parameterization describes acurve or ...
 21.1.2: In Exercises 14 decide if the parameterization describes acurve or ...
 21.1.3: In Exercises 14 decide if the parameterization describes acurve or ...
 21.1.4: In Exercises 14 decide if the parameterization describes acurve or ...
 21.1.5: Describe in words the objects parameterized by the equationsin Exer...
 21.1.6: Describe in words the objects parameterized by the equationsin Exer...
 21.1.7: Describe in words the objects parameterized by the equationsin Exer...
 21.1.8: Describe in words the objects parameterized by the equationsin Exer...
 21.1.9: In Exercises 912, for a sphere parameterized using the sphericalcoo...
 21.1.10: In Exercises 912, for a sphere parameterized using the sphericalcoo...
 21.1.11: In Exercises 912, for a sphere parameterized using the sphericalcoo...
 21.1.12: In Exercises 912, for a sphere parameterized using the sphericalcoo...
 21.1.13: In 1314, parameterize the plane that contains thethree points.(0, 0...
 21.1.14: In 1314, parameterize the plane that contains thethree points.(1, 2...
 21.1.15: In 1516, parameterize the plane through the pointwith the given nor...
 21.1.16: In 1516, parameterize the plane through the pointwith the given nor...
 21.1.17: Does the plane r (s, t) = (2 +s)i + (3 +s+t)j + 4tkcontain the foll...
 21.1.18: Are the following two planes parallel?x =2+ s + t, y =4+ s t, z =1+...
 21.1.19: In 1922, describe the families of parameter curveswith s = s0 and t...
 21.1.20: In 1922, describe the families of parameter curveswith s = s0 and t...
 21.1.21: In 1922, describe the families of parameter curveswith s = s0 and t...
 21.1.22: In 1922, describe the families of parameter curveswith s = s0 and t...
 21.1.23: A city is described parametrically by the equationr = (x0i + y0j + ...
 21.1.24: You are at a point on the earth with longitude 80 West ofGreenwich,...
 21.1.25: Describe in words the curve = /4 on the surface ofthe globe.
 21.1.26: Describe in words the curve = /4 on the surface ofthe globe.
 21.1.27: A decorative oak post is 48 long and is turned on a latheso that it...
 21.1.28: Find parametric equations for the sphere(x a)2 + (y b)2 + (z c)2 = ...
 21.1.29: Suppose you are standing at a point on the equator ofa sphere, para...
 21.1.30: Find parametric equations for the cone x2 +y2 = z2
 21.1.31: Parameterize the cone in Example 6 on page 1079 interms of r and .
 21.1.32: Give a parameterization of the circle of radius a centeredat the po...
 21.1.33: For 3335,(a) Write an equation in x, y, z and identify the parametr...
 21.1.34: For 3335,(a) Write an equation in x, y, z and identify the parametr...
 21.1.35: For 3335,(a) Write an equation in x, y, z and identify the parametr...
 21.1.36: In 3637, explain what is wrong with the statement.The parameter cur...
 21.1.37: In 3637, explain what is wrong with the statement.The parameter cur...
 21.1.38: In 3840, give an example of:A parameterization r (s, t) of the plan...
 21.1.39: In 3840, give an example of:An equation of the form f(x, y, z)=0 fo...
 21.1.40: In 3840, give an example of:A parameterized curve on the sphere r (...
 21.1.41: Are the statements in 4147 true or false? Give reasonsfor your answ...
 21.1.42: Are the statements in 4147 true or false? Give reasonsfor your answ...
 21.1.43: Are the statements in 4147 true or false? Give reasonsfor your answ...
 21.1.44: Are the statements in 4147 true or false? Give reasonsfor your answ...
 21.1.45: Are the statements in 4147 true or false? Give reasonsfor your answ...
 21.1.46: Are the statements in 4147 true or false? Give reasonsfor your answ...
 21.1.47: Are the statements in 4147 true or false? Give reasonsfor your answ...
 21.1.48: Match the parameterizations (I)(IV) with the surfaces(a)(d). In all...
Solutions for Chapter 21.1: COORDINATES AND PARAMETERIZED SURFACES
Full solutions for Calculus: Single and Multivariable  6th Edition
ISBN: 9780470888612
Solutions for Chapter 21.1: COORDINATES AND PARAMETERIZED SURFACES
Get Full SolutionsThis textbook survival guide was created for the textbook: Calculus: Single and Multivariable , edition: 6. This expansive textbook survival guide covers the following chapters and their solutions. Calculus: Single and Multivariable was written by and is associated to the ISBN: 9780470888612. Since 48 problems in chapter 21.1: COORDINATES AND PARAMETERIZED SURFACES have been answered, more than 43423 students have viewed full stepbystep solutions from this chapter. Chapter 21.1: COORDINATES AND PARAMETERIZED SURFACES includes 48 full stepbystep solutions.

Arccosecant function
See Inverse cosecant function.

Basic logistic function
The function ƒ(x) = 1 / 1 + ex

Combination
An arrangement of elements of a set, in which order is not important

Conditional probability
The probability of an event A given that an event B has already occurred

Continuous at x = a
lim x:a x a ƒ(x) = ƒ(a)

Cube root
nth root, where n = 3 (see Principal nth root),

De Moivre’s theorem
(r(cos ? + i sin ?))n = r n (cos n? + i sin n?)

Derivative of ƒ
The function defined by ƒ'(x) = limh:0ƒ(x + h)  ƒ(x)h for all of x where the limit exists

Focus, foci
See Ellipse, Hyperbola, Parabola.

Law of sines
sin A a = sin B b = sin C c

Multiplicative inverse of a real number
The reciprocal of b, or 1/b, b Z 0

nset
A set of n objects.

Polynomial in x
An expression that can be written in the form an x n + an1x n1 + Á + a1x + a0, where n is a nonnegative integer, the coefficients are real numbers, and an ? 0. The degree of the polynomial is n, the leading coefficient is an, the leading term is anxn, and the constant term is a0. (The number 0 is the zero polynomial)

Root of a number
See Principal nth root.

Slopeintercept form (of a line)
y = mx + b

Solve a triangle
To find one or more unknown sides or angles of a triangle

Sum of two vectors
<u1, u2> + <v1, v2> = <u1 + v1, u2 + v2> <u1 + v1, u2 + v2, u3 + v3>

Term of a polynomial (function)
An expression of the form anxn in a polynomial (function).

Translation
See Horizontal translation, Vertical translation.

Work
The product of a force applied to an object over a given distance W = ƒFƒ ƒAB!ƒ.