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# Solutions for Chapter 13: Vector-Valued Functions and Motion in Space ## Full solutions for Thomas' Calculus | 12th Edition

ISBN: 9780321587992 Solutions for Chapter 13: Vector-Valued Functions and Motion in Space

Solutions for Chapter 13
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##### ISBN: 9780321587992

Thomas' Calculus was written by Sieva Kozinsky and is associated to the ISBN: 9780321587992. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 13: Vector-Valued Functions and Motion in Space includes 32 full step-by-step solutions. Since 32 problems in chapter 13: Vector-Valued Functions and Motion in Space have been answered, more than 3170 students have viewed full step-by-step solutions from this chapter. This textbook survival guide was created for the textbook: Thomas' Calculus, edition: 12.

Key Calculus Terms and definitions covered in this textbook
• Cardioid

A limaçon whose polar equation is r = a ± a sin ?, or r = a ± a cos ?, where a > 0.

• Cosine

The function y = cos x

• Decreasing on an interval

A function f is decreasing on an interval I if, for any two points in I, a positive change in x results in a negative change in ƒ(x)

• Dihedral angle

An angle formed by two intersecting planes,

• Equivalent arrows

Arrows that have the same magnitude and direction.

• Equivalent systems of equations

Systems of equations that have the same solution.

• First octant

The points (x, y, z) in space with x > 0 y > 0, and z > 0.

• Half-angle identity

Identity involving a trigonometric function of u/2.

• Hypotenuse

Side opposite the right angle in a right triangle.

• Integrable over [a, b] Lba

ƒ1x2 dx exists.

• kth term of a sequence

The kth expression in the sequence

• Logarithmic re-expression of data

Transformation of a data set involving the natural logarithm: exponential regression, natural logarithmic regression, power regression

• Mode of a data set

The category or number that occurs most frequently in the set.

• n-set

A set of n objects.

• Ordered pair

A pair of real numbers (x, y), p. 12.

• 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.

• Pythagorean

Theorem In a right triangle with sides a and b and hypotenuse c, c2 = a2 + b2

• Sum of complex numbers

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

• x-coordinate

The directed distance from the y-axis yz-plane to a point in a plane (space), or the first number in an ordered pair (triple), pp. 12, 629.

• x-intercept

A point that lies on both the graph and the x-axis,.

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