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# Solutions for Chapter 4.6: Graph Sketching and Asymptotes ## Full solutions for Calculus: Early Transcendentals | 3rd Edition

ISBN: 9781464114885 Solutions for Chapter 4.6: Graph Sketching and Asymptotes

Solutions for Chapter 4.6
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##### ISBN: 9781464114885

Calculus: Early Transcendentals was written by and is associated to the ISBN: 9781464114885. This expansive textbook survival guide covers the following chapters and their solutions. Since 79 problems in chapter 4.6: Graph Sketching and Asymptotes have been answered, more than 41898 students have viewed full step-by-step solutions from this chapter. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals , edition: 3. Chapter 4.6: Graph Sketching and Asymptotes includes 79 full step-by-step solutions.

Key Calculus Terms and definitions covered in this textbook
• Absolute value of a real number

Denoted by |a|, represents the number a or the positive number -a if a < 0.

• Additive identity for the complex numbers

0 + 0i is the complex number zero

• Conjugate axis of a hyperbola

The line segment of length 2b that is perpendicular to the focal axis and has the center of the hyperbola as its midpoint

• Degree of a polynomial (function)

The largest exponent on the variable in any of the terms of the polynomial (function)

• Difference of two vectors

<u1, u2> - <v1, v2> = <u1 - v1, u2 - v2> or <u1, u2, u3> - <v1, v2, v3> = <u1 - v1, u2 - v2, u3 - v3>

• Double inequality

A statement that describes a bounded interval, such as 3 ? x < 5

• Focal axis

The line through the focus and perpendicular to the directrix of a conic.

• Irreducible quadratic over the reals

A quadratic polynomial with real coefficients that cannot be factored using real coefficients.

• Linear factorization theorem

A polynomial ƒ(x) of degree n > 0 has the factorization ƒ(x) = a(x1 - z1) 1x - i z 22 Á 1x - z n where the z1 are the zeros of ƒ

• Linear regression

A procedure for finding the straight line that is the best fit for the data

• Nautical mile

Length of 1 minute of arc along the Earth’s equator.

• Parabola

The graph of a quadratic function, or the set of points in a plane that are equidistant from a fixed point (the focus) and a fixed line (the directrix).

• Quotient rule of logarithms

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

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.

• Real number line

A horizontal line that represents the set of real numbers.

• Semimajor axis

The distance from the center to a vertex of an ellipse.

• Sinusoid

A function that can be written in the form f(x) = a sin (b (x - h)) + k or f(x) = a cos (b(x - h)) + k. The number a is the amplitude, and the number h is the phase shift.

• Solve a triangle

To find one or more unknown sides or angles of a triangle

• Solve by substitution

Method for solving systems of linear equations.

• y-intercept

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

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