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# Solutions for Chapter 4: Maxima and Minima in Several Variables ## Full solutions for Vector Calculus | 4th Edition

ISBN: 9780321780652 Solutions for Chapter 4: Maxima and Minima in Several Variables

Solutions for Chapter 4
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##### ISBN: 9780321780652

Chapter 4: Maxima and Minima in Several Variables includes 30 full step-by-step solutions. Vector Calculus was written by and is associated to the ISBN: 9780321780652. This textbook survival guide was created for the textbook: Vector Calculus, edition: 4. Since 30 problems in chapter 4: Maxima and Minima in Several Variables have been answered, more than 12867 students have viewed full step-by-step solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions.

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

A triangle in which all angles measure less than 90°

• Additive inverse of a real number

The opposite of b , or -b

• Coefficient of determination

The number r2 or R2 that measures how well a regression curve fits the data

• Damping factor

The factor Ae-a in an equation such as y = Ae-at cos bt

• Equivalent equations (inequalities)

Equations (inequalities) that have the same solutions.

• Frequency distribution

See Frequency table.

• Hyperbola

A set of points in a plane, the absolute value of the difference of whose distances from two fixed points (the foci) is a constant.

• Identity properties

a + 0 = a, a ? 1 = a

• Intermediate Value Theorem

If ƒ is a polynomial function and a < b , then ƒ assumes every value between ƒ(a) and ƒ(b).

See Polynomial function in x.

• Multiplication principle of probability

If A and B are independent events, then P(A and B) = P(A) # P(B). If Adepends on B, then P(A and B) = P(A|B) # P(B)

• Pythagorean identities

sin2 u + cos2 u = 1, 1 + tan2 u = sec2 u, and 1 + cot2 u = csc2 u

• Quotient rule of logarithms

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

• Rational zeros

Zeros of a function that are rational numbers.

• Residual

The difference y1 - (ax 1 + b), where (x1, y1)is a point in a scatter plot and y = ax + b is a line that fits the set of data.

• Riemann sum

A sum where the interval is divided into n subintervals of equal length and is in the ith subinterval.

• Sequence of partial sums

The sequence {Sn} , where Sn is the nth partial sum of the series, that is, the sum of the first n terms of the series.

• Standard unit vectors

In the plane i = <1, 0> and j = <0,1>; in space i = <1,0,0>, j = <0,1,0> k = <0,0,1>

• Time plot

A line graph in which time is measured on the horizontal axis.

• Triangular number

A number that is a sum of the arithmetic series 1 + 2 + 3 + ... + n for some natural number n.

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