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Get Full Access to Calculus - Textbook Survival Guide
Get Full Access to Calculus - Textbook Survival Guide
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# Solutions for Chapter 13.5: Chain Rules for Functions of Several Variables

## Full solutions for Calculus | 8th Edition

ISBN: 9780618502981

Solutions for Chapter 13.5: Chain Rules for Functions of Several Variables

Solutions for Chapter 13.5
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##### ISBN: 9780618502981

Calculus was written by and is associated to the ISBN: 9780618502981. Since 64 problems in chapter 13.5: Chain Rules for Functions of Several Variables have been answered, more than 78032 students have viewed full step-by-step solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 13.5: Chain Rules for Functions of Several Variables includes 64 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 vector

See Magnitude of a vector.

• Arrow

The notation PQ denoting the directed line segment with initial point P and terminal point Q.

• Compound interest

Interest that becomes part of the investment

• Compounded monthly

See Compounded k times per year.

• Directrix of a parabola, ellipse, or hyperbola

A line used to determine the conic

• Focal width of a parabola

The length of the chord through the focus and perpendicular to the axis.

• Limaçon

A graph of a polar equation r = a b sin u or r = a b cos u with a > 0 b > 0

• Natural logarithm

A logarithm with base e.

• Natural logarithmic function

The inverse of the exponential function y = ex, denoted by y = ln x.

• Numerical derivative of ƒ at a

NDER f(a) = ƒ1a + 0.0012 - ƒ1a - 0.00120.002

• Outcomes

The various possible results of an experiment.

• Partial fractions

The process of expanding a fraction into a sum of fractions. The sum is called the partial fraction decomposition of the original fraction.

• 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).

• Real zeros

Zeros of a function that are real numbers.

• Rigid transformation

A transformation that leaves the basic shape of a graph unchanged.

• RRAM

A Riemann sum approximation of the area under a curve ƒ(x) from x = a to x = b using x1 as the right-hand end point of each subinterval.

• Sine

The function y = sin x.

• Stretch of factor c

A transformation of a graph obtained by multiplying all the x-coordinates (horizontal stretch) by the constant 1/c, or all of the y-coordinates (vertical stretch) of the points by a constant c, c, > 1.

• symmetric about the x-axis

A graph in which (x, -y) is on the graph whenever (x, y) is; or a graph in which (r, -?) or (-r, ?, -?) is on the graph whenever (r, ?) is

• z-axis

Usually the third dimension in Cartesian space.

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