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# Solutions for Chapter 2: Differentiation ## Full solutions for Vector Calculus | 6th Edition

ISBN: 9781429215084 Solutions for Chapter 2: Differentiation

Solutions for Chapter 2
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##### ISBN: 9781429215084

Vector Calculus was written by and is associated to the ISBN: 9781429215084. This textbook survival guide was created for the textbook: Vector Calculus, edition: 6. Chapter 2: Differentiation includes 35 full step-by-step solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 35 problems in chapter 2: Differentiation have been answered, more than 3030 students have viewed full step-by-step solutions from this chapter.

Key Calculus Terms and definitions covered in this textbook
• Associative properties

a + (b + c) = (a + b) + c, a(bc) = (ab)c.

• Combinatorics

A branch of mathematics related to determining the number of elements of a set or the number of ways objects can be arranged or combined

• Complements or complementary angles

Two angles of positive measure whose sum is 90°

• Compounded continuously

Interest compounded using the formula A = Pert

• Cotangent

The function y = cot x

• Cube root

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

• Division

a b = aa 1 b b, b Z 0

• Horizontal translation

A shift of a graph to the left or right.

• Implied domain

The domain of a function’s algebraic expression.

• Multiplication property of equality

If u = v and w = z, then uw = vz

• Multiplicative inverse of a real number

The reciprocal of b, or 1/b, b Z 0

• Nonsingular matrix

A square matrix with nonzero determinant

• Probability function

A function P that assigns a real number to each outcome O in a sample space satisfying: 0 … P1O2 … 1, P12 = 0, and the sum of the probabilities of all outcomes is 1.

• Quotient identities

tan ?= sin ?cos ?and cot ?= cos ? sin ?

• Re-expression of data

A transformation of a data set.

• Real zeros

Zeros of a function that are real numbers.

• Relevant domain

The portion of the domain applicable to the situation being modeled.

• Rigid transformation

A transformation that leaves the basic shape of a graph unchanged.

• Solve by substitution

Method for solving systems of linear equations.

• Vector equation for a line in space

The line through P0(x 0, y0, z0) in the direction of the nonzero vector V = <a, b, c> has vector equation r = r0 + tv , where r = <x,y,z>.

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