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# Solutions for Chapter 6: Derivatives

## Full solutions for Calculus: Early Transcendentals | 1st Edition

ISBN: 9780321570567

Solutions for Chapter 6: Derivatives

Solutions for Chapter 6
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##### ISBN: 9780321570567

Summary of Chapter 6: Derivatives

We use limits not only to define the derivative but also to develop efficient rules for finding derivatives. The applications of the derivative—which we introduce along the way—are endless because almost everything around us is in a state of change, and derivatives describe change.

This expansive textbook survival guide covers the following chapters and their solutions. Chapter 6: Derivatives includes 9 full step-by-step solutions. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. Since 9 problems in chapter 6: Derivatives have been answered, more than 411890 students have viewed full step-by-step solutions from this chapter.

Key Calculus Terms and definitions covered in this textbook
• Directed line segment

See Arrow.

• Distance (in a coordinate plane)

The distance d(P, Q) between P(x, y) and Q(x, y) d(P, Q) = 2(x 1 - x 2)2 + (y1 - y2)2

• Division algorithm for polynomials

Given ƒ(x), d(x) ? 0 there are unique polynomials q1x (quotient) and r1x(remainder) ƒ1x2 = d1x2q1x2 + r1x2 with with either r1x2 = 0 or degree of r(x) 6 degree of d1x2

• equation of a hyperbola

(x - h)2 a2 - (y - k)2 b2 = 1 or (y - k)2 a2 - (x - h)2 b2 = 1

• Equivalent equations (inequalities)

Equations (inequalities) that have the same solutions.

• Focal width of a parabola

The length of the chord through the focus and perpendicular to the axis.

• Horizontal component

See Component form of a vector.

• Identity properties

a + 0 = a, a ? 1 = a

• Infinite discontinuity at x = a

limx:a + x a ƒ(x) = q6 or limx:a - ƒ(x) = q.

• Initial point

See Arrow.

• Positive angle

Angle generated by a counterclockwise rotation.

• 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

A function that can be written in the form ƒ(x) = ax 2 + bx + c, where a, b, and c are real numbers, and a ? 0.

• RRAM

A Riemann sum approximation of the area under a curve ƒ(x) from x = a to x = b using x1 as the right-hand end point of each subinterval.

• Sine

The function y = sin x.

A graph in which (-x, y) is on the graph whenever (x, y) is; or a graph in which (-r, -?) or (r, ?, -?) is on the graph whenever (r, ?) is

• Term of a polynomial (function)

An expression of the form anxn in a polynomial (function).

• Variable (in statistics)

A characteristic of individuals that is being identified or measured.

• Work

The product of a force applied to an object over a given distance W = ƒFƒ ƒAB!ƒ.

• y-intercept

A point that lies on both the graph and the y-axis.