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# Solutions for Chapter 12.7: Cylindrical and Spherical Coordinates ## Full solutions for Calculus: Early Transcendentals | 3rd Edition

ISBN: 9781464114885 Solutions for Chapter 12.7: Cylindrical and Spherical Coordinates

Solutions for Chapter 12.7
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##### ISBN: 9781464114885

Chapter 12.7: Cylindrical and Spherical Coordinates includes 88 full step-by-step solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals , edition: 3. Since 88 problems in chapter 12.7: Cylindrical and Spherical Coordinates have been answered, more than 41987 students have viewed full step-by-step solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9781464114885.

Key Calculus Terms and definitions covered in this textbook
• Aphelion

The farthest point from the Sun in a planet’s orbit

• Component form of a vector

If a vector’s representative in standard position has a terminal point (a,b) (or (a, b, c)) , then (a,b) (or (a, b, c)) is the component form of the vector, and a and b are the horizontal and vertical components of the vector (or a, b, and c are the x-, y-, and z-components of the vector, respectively)

• Compounded k times per year

Interest compounded using the formula A = Pa1 + rkbkt where k = 1 is compounded annually, k = 4 is compounded quarterly k = 12 is compounded monthly, etc.

• Directed distance

See Polar coordinates.

• Distance (in Cartesian space)

The distance d(P, Q) between and P(x, y, z) and Q(x, y, z) or d(P, Q) ((x ) - x 2)2 + (y1 - y2)2 + (z 1 - z 2)2

• End behavior asymptote of a rational function

A polynomial that the function approaches as.

• Extraneous solution

Any solution of the resulting equation that is not a solution of the original equation.

• General form (of a line)

Ax + By + C = 0, where A and B are not both zero.

• Geometric sequence

A sequence {an}in which an = an-1.r for every positive integer n ? 2. The nonzero number r is called the common ratio.

• Geometric series

A series whose terms form a geometric sequence.

• Horizontal line

y = b.

• Independent variable

Variable representing the domain value of a function (usually x).

• Inductive step

See Mathematical induction.

• Measure of center

A measure of the typical, middle, or average value for a data set

• Negative association

A relationship between two variables in which higher values of one variable are generally associated with lower values of the other variable.

• Octants

The eight regions of space determined by the coordinate planes.

• Product of a scalar and a vector

The product of scalar k and vector u = 8u1, u29 1or u = 8u1, u2, u392 is k.u = 8ku1, ku291or k # u = 8ku1, ku2, ku392,

• Range screen

See Viewing window.

• Sum of complex numbers

(a + bi) + (c + di) = (a + c) + (b + d)i

• Triangular number

A number that is a sum of the arithmetic series 1 + 2 + 3 + ... + n for some natural number n.

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