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# Solutions for Chapter 12: Vector-Valued Functions ## Full solutions for Calculus | 9th Edition

ISBN: 9780547167022 Solutions for Chapter 12: Vector-Valued Functions

Solutions for Chapter 12
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##### ISBN: 9780547167022

Calculus was written by and is associated to the ISBN: 9780547167022. This expansive textbook survival guide covers the following chapters and their solutions. Since 78 problems in chapter 12: Vector-Valued Functions have been answered, more than 36227 students have viewed full step-by-step solutions from this chapter. Chapter 12: Vector-Valued Functions includes 78 full step-by-step solutions. This textbook survival guide was created for the textbook: Calculus , edition: 9.

Key Calculus Terms and definitions covered in this textbook
• Acute angle

An angle whose measure is between 0° and 90°

• Arrow

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

• Bounded above

A function is bounded above if there is a number B such that ƒ(x) ? B for all x in the domain of ƒ.

• Composition of functions

(f ? g) (x) = f (g(x))

• Conic section (or conic)

A curve obtained by intersecting a double-napped right circular cone with a plane

• Direction of an arrow

The angle the arrow makes with the positive x-axis

• Ellipse

The set of all points in the plane such that the sum of the distances from a pair of fixed points (the foci) is a constant

• Geometric sequence

A sequence {an}in which an = an-1.r for every positive integer n ? 2. The nonzero number r is called the common ratio.

• Higher-degree polynomial function

A polynomial function whose degree is ? 3

• 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

• Initial point

See Arrow.

• Initial side of an angle

See Angle.

• Line graph

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

• Mean (of a set of data)

The sum of all the data divided by the total number of items

• Root of an equation

A solution.

• Row operations

See Elementary row operations.

• Sum of a finite arithmetic series

Sn = na a1 + a2 2 b = n 2 32a1 + 1n - 12d4,

• Terms of a sequence

The range elements of a sequence.

• Translation

See Horizontal translation, Vertical translation.

• Unit vector

Vector of length 1.

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