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# Solutions for Chapter 12.6: LIMITS AND CONTINUITY ## Full solutions for Calculus: Single and Multivariable | 6th Edition

ISBN: 9780470888612 Solutions for Chapter 12.6: LIMITS AND CONTINUITY

Solutions for Chapter 12.6
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##### ISBN: 9780470888612

This expansive textbook survival guide covers the following chapters and their solutions. Chapter 12.6: LIMITS AND CONTINUITY includes 30 full step-by-step solutions. Calculus: Single and Multivariable was written by and is associated to the ISBN: 9780470888612. This textbook survival guide was created for the textbook: Calculus: Single and Multivariable , edition: 6. Since 30 problems in chapter 12.6: LIMITS AND CONTINUITY have been answered, more than 45033 students have viewed full step-by-step solutions from this chapter.

Key Calculus Terms and definitions covered in this textbook
• Acceleration due to gravity

g ? 32 ft/sec2 ? 9.8 m/sec

• 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.

• Conversion factor

A ratio equal to 1, used for unit conversion

• Cube root

nth root, where n = 3 (see Principal nth root),

• Divergence

A sequence or series diverges if it does not converge

• Domain of a function

The set of all input values for a function

• 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

• Future value of an annuity

The net amount of money returned from an annuity.

• Gaussian elimination

A method of solving a system of n linear equations in n unknowns.

• Linear inequality in x

An inequality that can be written in the form ax + b < 0 ,ax + b … 0 , ax + b > 0, or ax + b Ú 0, where a and b are real numbers and a Z 0

• Linear regression equation

Equation of a linear regression line

• Logistic growth function

A model of population growth: ƒ1x2 = c 1 + a # bx or ƒ1x2 = c1 + ae-kx, where a, b, c, and k are positive with b < 1. c is the limit to growth

• Magnitude of a vector

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

• Numerical derivative of ƒ at a

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

• Product of complex numbers

(a + bi)(c + di) = (ac - bd) + (ad + bc)i

• Pseudo-random numbers

Computer-generated numbers that can be used to approximate true randomness in scientific studies. Since they depend on iterative computer algorithms, they are not truly random

• Rational numbers

Numbers that can be written as a/b, where a and b are integers, and b ? 0.

• Simple harmonic motion

Motion described by d = a sin wt or d = a cos wt

• Unbounded interval

An interval that extends to -? or ? (or both).

• Upper bound for ƒ

Any number B for which ƒ(x) ? B for all x in the domain of ƒ.

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