×
×

# 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
4 5 0 407 Reviews
26
5
##### ISBN: 9780321587992

Thomas' Calculus was written by 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 10641 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
• Absolute value of a complex number

The absolute value of the complex number z = a + b is given by ?a2+b2; also, the length of the segment from the origin to z in the complex plane.

• Deductive reasoning

The process of utilizing general information to prove a specific hypothesis

• Differentiable at x = a

ƒ'(a) exists

• Irrational zeros

Zeros of a function that are irrational numbers.

• Line graph

A graph of data in which consecutive data points are connected by line segments

• Line of travel

The path along which an object travels

• Magnitude of a vector

The magnitude of <a, b> is 2a2 + b2. The magnitude of <a, b, c> is 2a2 + b2 + c2

• Natural logarithm

A logarithm with base e.

• Open interval

An interval that does not include its endpoints.

• Parallelogram representation of vector addition

Geometric representation of vector addition using the parallelogram determined by the position vectors.

• Parametric equations for a line in space

The line through P0(x 0, y0, z 0) in the direction of the nonzero vector v = <a, b, c> has parametric equations x = x 0 + at, y = y 0 + bt, z = z0 + ct.

• 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,

• Series

A finite or infinite sum of terms.

• Shrink of factor c

A transformation of a graph obtained by multiplying all the x-coordinates (horizontal shrink) by the constant 1/c or all of the y-coordinates (vertical shrink) by the constant c, 0 < c < 1.

• Venn diagram

A visualization of the relationships among events within a sample space.

• Vertex of a cone

See Right circular cone.

• Vertical translation

A shift of a graph up or down.

• Weighted mean

A mean calculated in such a way that some elements of the data set have higher weights (that is, are counted more strongly in determining the mean) than others.

• Ymax

The y-value of the top of the viewing window.

• Ymin

The y-value of the bottom of the viewing window.

×