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# Solutions for Chapter 4.4: Some Applications of Extrema

## Full solutions for Vector Calculus | 4th Edition

ISBN: 9780321780652

Solutions for Chapter 4.4: Some Applications of Extrema

Solutions for Chapter 4.4
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##### ISBN: 9780321780652

Since 16 problems in chapter 4.4: Some Applications of Extrema have been answered, more than 13594 students have viewed full step-by-step solutions from this chapter. Chapter 4.4: Some Applications of Extrema includes 16 full step-by-step solutions. Vector Calculus was written by and is associated to the ISBN: 9780321780652. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Vector Calculus, edition: 4.

Key Calculus Terms and definitions covered in this textbook
• Blind experiment

An experiment in which subjects do not know if they have been given an active treatment or a placebo

• Cardioid

A limaçon whose polar equation is r = a ± a sin ?, or r = a ± a cos ?, where a > 0.

• Combination

An arrangement of elements of a set, in which order is not important

• Common ratio

See Geometric sequence.

• De Moivre’s theorem

(r(cos ? + i sin ?))n = r n (cos n? + i sin n?)

• Divergence

A sequence or series diverges if it does not converge

• Graph of an inequality in x and y

The set of all points in the coordinate plane corresponding to the solutions x, y of the inequality.

• Inverse variation

See Power function.

• Matrix, m x n

A rectangular array of m rows and n columns of real numbers

• nth root

See Principal nth root

• Numerical derivative of ƒ at a

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

• Obtuse triangle

A triangle in which one angle is greater than 90°.

• Placebo

In an experimental study, an inactive treatment that is equivalent to the active treatment in every respect except for the factor about which an inference is to be made. Subjects in a blind experiment do not know if they have been given the active treatment or the placebo.

• Polar distance formula

The distance between the points with polar coordinates (r1, ?1 ) and (r2, ?2 ) = 2r 12 + r 22 - 2r1r2 cos 1?1 - ?22

• Power function

A function of the form ƒ(x) = k . x a, where k and a are nonzero constants. k is the constant of variation and a is the power.

• Rational zeros

Zeros of a function that are rational numbers.

• Right angle

A 90° angle.

• Row echelon form

A matrix in which rows consisting of all 0’s occur only at the bottom of the matrix, the first nonzero entry in any row with nonzero entries is 1, and the leading 1’s move to the right as we move down the rows.

• Solution of a system in two variables

An ordered pair of real numbers that satisfies all of the equations or inequalities in the system

• Terms of a sequence

The range elements of a sequence.

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