Explanation Concept: a) Domain of the function is set of all the possible values where the given function is defined. b) For any rational function f ( x ) = p ( x ) q ( x ) , where p ( x ) and q ( x ) are polynomial with no common factors other than constants, if α is a zero of the denominator, then the line x = α is a vertical asymptote for the graph of the function. c) If the degree of the numerator and denominator in a rational function is same, horizontal asymptote is given by y = a b , where a and b is the leading coefficients of numerator and denominator respectively. d) For any rational function f ( x ) = p ( x ) q ( x ) , if the degree of p ( x ) is less than q ( x ) then horizontal asymptotes is given by y = 0 or x -axis. e) For any rational function f ( x ) = p ( x ) q ( x ) , if the degree of p ( x ) is greater than q ( x ) then, there will be no horizontal asymptotes. f) In a rational function f ( x ) = p ( x ) q ( x ) , the degree of p ( x ) is greater than q ( x ) by one degree, then the asymptotes obtained are called oblique asymptotes. Factorize the function f ( x ) .

5th Edition

ISBN: 9780321969576

Author: Judith A. Beecher, Judith A. Penna, Marvin L. Bittinger

Publisher: PEARSON

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Chapter 4.5, Problem 77E

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The graph of the function f(x)=x2x2−x−2 and label all the asymptotes. Also find domain, x and y intercept of the graph.

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Chapter 4.5, Problem 76E

Chapter 4.5, Problem 78E

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(20 p) 1. Find a particular solution satisfying the given initial conditions for the third-order homogeneous linear equation given below. (See Section 5.2 in your textbook if you need a review of the subject.) y(3)+2y"-y-2y = 0; y(0) = 1, y'(0) = 2, y"(0) = 0; y₁ = e*, y2 = e¯x, y3 = e−2x (20 p) 2. Find a particular solution satisfying the given initial conditions for the second-order nonhomogeneous linear equation given below. (See Section 5.2 in your textbook if you need a review of the subject.) y"-2y-3y = 6; y(0) = 3, y'(0) = 11 yc = c₁ex + c2e³x; yp = −2 (60 p) 3. Find the general, and if possible, particular solutions of the linear systems of differential equations given below using the eigenvalue-eigenvector method. (See Section 7.3 in your textbook if you need a review of the subject.) = a) x 4x1 + x2, x2 = 6x1-x2 b) x=6x17x2, x2 = x1-2x2 c) x = 9x1+5x2, x2 = −6x1-2x2; x1(0) = 1, x2(0)=0

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Chapter 4 Solutions

College Algebra (5th Edition)

Ch. 4.1 - Determine the leading term, the leading...Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E Ch. 4.1 - Prob. 7E Ch. 4.1 - Prob. 8E Ch. 4.1 - Prob. 9E Ch. 4.1 - Prob. 10E

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To plot: The graph of the function f ( x ) = x 2 x 2 − x − 2 and label all the asymptotes. Also find domain, x and y intercept of the graph.

To plot: The graph of the function f(x)=x2x2−x−2 and label all the asymptotes. Also find domain, x and y intercept of the graph.

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Chapter 4 Solutions

To plot:

The graph of the function f(x)=x2x2−x−2 and label all the asymptotes. Also find domain, x and y intercept of the graph.