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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 Patricia 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 21415 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
• Central angle

An angle whose vertex is the center of a circle

• Conditional probability

The probability of an event A given that an event B has already occurred

• Double inequality

A statement that describes a bounded interval, such as 3 ? x < 5

• Explicitly defined sequence

A sequence in which the kth term is given as a function of k.

• Geometric series

A series whose terms form a geometric sequence.

• Increasing on an interval

A function ƒ is increasing on an interval I if, for any two points in I, a positive change in x results in a positive change in.

• Initial side of an angle

See Angle.

• Limit at infinity

limx: qƒ1x2 = L means that ƒ1x2 gets arbitrarily close to L as x gets arbitrarily large; lim x:- q ƒ1x2 means that gets arbitrarily close to L as gets arbitrarily large

• Maximum r-value

The value of |r| at the point on the graph of a polar equation that has the maximum distance from the pole

• Minor axis

The perpendicular bisector of the major axis of an ellipse with endpoints on the ellipse.

• Multiplicative inverse of a complex number

The reciprocal of a + bi, or 1 a + bi = a a2 + b2- ba2 + b2 i

• Numerical derivative of ƒ at a

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

• Periodic function

A function ƒ for which there is a positive number c such that for every value t in the domain of ƒ. The smallest such number c is the period of the function.

• Positive association

A relationship between two variables in which higher values of one variable are generally associated with higher values of the other variable, p. 717.

• Rational expression

An expression that can be written as a ratio of two polynomials.

• Rectangular coordinate system

See Cartesian coordinate system.

• Root of an equation

A solution.

• Speed

The magnitude of the velocity vector, given by distance/time.

• Transitive property

If a = b and b = c , then a = c. Similar properties hold for the inequality symbols <, >, ?, ?.

• xz-plane

The points x, 0, z in Cartesian space.

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