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# Solutions for Chapter 11.7: Cylindrical and Spherical Coordinates

## Full solutions for Calculus | 8th Edition

ISBN: 9780618502981

Solutions for Chapter 11.7: Cylindrical and Spherical Coordinates

Solutions for Chapter 11.7
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##### ISBN: 9780618502981

Since 124 problems in chapter 11.7: Cylindrical and Spherical Coordinates have been answered, more than 82198 students have viewed full step-by-step solutions from this chapter. Calculus was written by and is associated to the ISBN: 9780618502981. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 11.7: Cylindrical and Spherical Coordinates includes 124 full step-by-step solutions. This textbook survival guide was created for the textbook: Calculus, edition: 8.

Key Calculus Terms and definitions covered in this textbook
• Absolute value of a real number

Denoted by |a|, represents the number a or the positive number -a if a < 0.

• Bounded

A function is bounded if there are numbers b and B such that b ? ƒ(x) ? B for all x in the domain of f.

• Constant function (on an interval)

ƒ(x 1) = ƒ(x 2) x for any x1 and x2 (in the interval)

• Cosine

The function y = cos x

• Directrix of a parabola, ellipse, or hyperbola

A line used to determine the conic

• Double-angle identity

An identity involving a trigonometric function of 2u

• Inverse sine function

The function y = sin-1 x

• Invertible linear system

A system of n linear equations in n variables whose coefficient matrix has a nonzero determinant.

• Matrix, m x n

A rectangular array of m rows and n columns of real numbers

A measure that tells how widely distributed data are.

• Opens upward or downward

A parabola y = ax 2 + bx + c opens upward if a > 0 and opens downward if a < 0.

• Outcomes

The various possible results of an experiment.

• Random numbers

Numbers that can be used by researchers to simulate randomness in scientific studies (they are usually obtained from lengthy tables of decimal digits that have been generated by verifiably random natural phenomena).

• Rational zeros theorem

A procedure for finding the possible rational zeros of a polynomial.

• Resistant measure

A statistical measure that does not change much in response to outliers.

• Sinusoidal regression

A procedure for fitting a curve y = a sin (bx + c) + d to a set of data

• Solve by substitution

Method for solving systems of linear equations.

• Summation notation

The series a nk=1ak, where n is a natural number ( or ?) is in summation notation and is read "the sum of ak from k = 1 to n(or infinity).” k is the index of summation, and ak is the kth term of the series

• Vector

An ordered pair <a, b> of real numbers in the plane, or an ordered triple <a, b, c> of real numbers in space. A vector has both magnitude and direction.

• Vertices of an ellipse

The points where the ellipse intersects its focal axis.

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