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# Solutions for Chapter 12.PE: University Calculus: Early Transcendentals 2nd Edition ## Full solutions for University Calculus: Early Transcendentals | 2nd Edition

ISBN: 9780321717399 Solutions for Chapter 12.PE

Solutions for Chapter 12.PE
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##### ISBN: 9780321717399

Since 32 problems in chapter 12.PE have been answered, more than 57576 students have viewed full step-by-step solutions from this chapter. Chapter 12.PE includes 32 full step-by-step solutions. This expansive textbook survival guide covers the following chapters and their solutions. University Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321717399. This textbook survival guide was created for the textbook: University Calculus: Early Transcendentals , edition: 2.

Key Calculus Terms and definitions covered in this textbook
• Additive identity for the complex numbers

0 + 0i is the complex number zero

• Angle between vectors

The angle formed by two nonzero vectors sharing a common initial point

• Arc length formula

The length of an arc in a circle of radius r intercepted by a central angle of u radians is s = r u.

• Binomial probability

In an experiment with two possible outcomes, the probability of one outcome occurring k times in n independent trials is P1E2 = n!k!1n - k2!pk11 - p) n-k where p is the probability of the outcome occurring once

• Characteristic polynomial of a square matrix A

det(xIn - A), where A is an n x n matrix

• Difference of complex numbers

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

• Equivalent equations (inequalities)

Equations (inequalities) that have the same solutions.

• Half-angle identity

Identity involving a trigonometric function of u/2.

• Histogram

A graph that visually represents the information in a frequency table using rectangular areas proportional to the frequencies.

• Hyperboloid of revolution

A surface generated by rotating a hyperbola about its transverse axis, p. 607.

• Invertible linear system

A system of n linear equations in n variables whose coefficient matrix has a nonzero determinant.

• Ordered pair

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

• Outcomes

The various possible results of an experiment.

• Quotient rule of logarithms

logb a R S b = logb R - logb S, R > 0, S > 0

• Randomization

The principle of experimental design that makes it possible to use the laws of probability when making inferences.

• Real axis

See Complex plane.

• Real number line

A horizontal line that represents the set of real numbers.

• Real zeros

Zeros of a function that are real numbers.

• Scientific notation

A positive number written as c x 10m, where 1 ? c < 10 and m is an integer.

• Slope

Ratio change in y/change in x

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