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# Solutions for Chapter 12.1: Vector-Valued Functions

## Full solutions for Calculus | 8th Edition

ISBN: 9780618502981

Solutions for Chapter 12.1: Vector-Valued Functions

Solutions for Chapter 12.1
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##### ISBN: 9780618502981

Calculus was written by and is associated to the ISBN: 9780618502981. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 12.1: Vector-Valued Functions includes 92 full step-by-step solutions. Since 92 problems in chapter 12.1: Vector-Valued Functions have been answered, more than 76558 students have viewed full step-by-step solutions from this chapter. This textbook survival guide was created for the textbook: Calculus, edition: 8.

Key Calculus Terms and definitions covered in this textbook

P(A or B) = P(A) + P(B) - P(A and B). If A and B are mutually exclusive events, then P(A or B) = P(A) + P(B)

• Binomial coefficients

The numbers in Pascal’s triangle: nCr = anrb = n!r!1n - r2!

• Cosine

The function y = cos x

• Factoring (a polynomial)

Writing a polynomial as a product of two or more polynomial factors.

• Horizontal asymptote

The line is a horizontal asymptote of the graph of a function ƒ if lim x:- q ƒ(x) = or lim x: q ƒ(x) = b

• Imaginary part of a complex number

See Complex number.

• Leaf

The final digit of a number in a stemplot.

• Negative linear correlation

See Linear correlation.

• Plane in Cartesian space

The graph of Ax + By + Cz + D = 0, where A, B, and C are not all zero.

• Principal nth root

If bn = a, then b is an nth root of a. If bn = a and a and b have the same sign, b is the principal nth root of a (see Radical), p. 508.

• Probability distribution

The collection of probabilities of outcomes in a sample space assigned by a probability function.

• Right triangle

A triangle with a 90° angle.

• Solve an equation or inequality

To find all solutions of the equation or inequality

• Square matrix

A matrix whose number of rows equals the number of columns.

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

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

• Third quartile

See Quartile.

• Triangular number

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

• Vector equation for a line in space

The line through P0(x 0, y0, z0) in the direction of the nonzero vector V = <a, b, c> has vector equation r = r0 + tv , where r = <x,y,z>.

• Zero factorial

See n factorial.

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