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# Solutions for Chapter 3: The Derivative ## Full solutions for Calculus:Early Transcendentals | 7th Edition

ISBN: 9780131569898 Solutions for Chapter 3: The Derivative

Solutions for Chapter 3
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##### ISBN: 9780131569898

Summary of Chapter 3: The Derivative

The definition of the derivative. The rate of change of a function with respect to a variable. Operator notation for derivatives.

This expansive textbook survival guide covers the following chapters and their solutions. Chapter 3: The Derivative includes 125 full step-by-step solutions. This textbook survival guide was created for the textbook: Calculus:Early Transcendentals, edition: 7. Calculus:Early Transcendentals was written by and is associated to the ISBN: 9780131569898. Since 125 problems in chapter 3: The Derivative have been answered, more than 40233 students have viewed full step-by-step solutions from this chapter.

Key Calculus Terms and definitions covered in this textbook
• Arrow

The notation PQ denoting the directed line segment with initial point P and terminal point Q.

• Back-to-back stemplot

A stemplot with leaves on either side used to compare two distributions.

• Base

See Exponential function, Logarithmic function, nth power of a.

• Definite integral

The definite integral of the function ƒ over [a,b] is Lbaƒ(x) dx = limn: q ani=1 ƒ(xi) ¢x provided the limit of the Riemann sums exists

• Exponential growth function

Growth modeled by ƒ(x) = a ? b a > 0, b > 1 .

• Focus, foci

See Ellipse, Hyperbola, Parabola.

• Graph of a relation

The set of all points in the coordinate plane corresponding to the ordered pairs of the relation.

• Imaginary part of a complex number

See Complex number.

• Inverse composition rule

The composition of a one-toone function with its inverse results in the identity function.

• Jump discontinuity at x a

limx:a - ƒ1x2 and limx:a + ƒ1x2 exist but are not equal

• Length of a vector

See Magnitude of a vector.

• Mean (of a set of data)

The sum of all the data divided by the total number of items

• Number line graph of a linear inequality

The graph of the solutions of a linear inequality (in x) on a number line

• Phase shift

See Sinusoid.

• Polynomial in x

An expression that can be written in the form an x n + an-1x n-1 + Á + a1x + a0, where n is a nonnegative integer, the coefficients are real numbers, and an ? 0. The degree of the polynomial is n, the leading coefficient is an, the leading term is anxn, and the constant term is a0. (The number 0 is the zero polynomial)

The measure of an angle in radians, or, for a central angle, the ratio of the length of the intercepted arc tothe radius of the circle.

• Scatter plot

A plot of all the ordered pairs of a two-variable data set on a coordinate plane.

• Tangent line of ƒ at x = a

The line through (a, ƒ(a)) with slope ƒ'(a) provided ƒ'(a) exists.

• Unbounded interval

An interval that extends to -? or ? (or both).

• Zero factor property

If ab = 0 , then either a = 0 or b = 0.