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Get Full Access to Fundamentals Of Differential Equations - 8 Edition - Chapter 5.4 - Problem 30e
Get Full Access to Fundamentals Of Differential Equations - 8 Edition - Chapter 5.4 - Problem 30e

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# A proof of Theorem 1, page 268, is outlined below. The ISBN: 9780321747730 43

## Solution for problem 30E Chapter 5.4

Fundamentals of Differential Equations | 8th Edition

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Problem 30E

Problem 30E

A proof of Theorem 1, page 268, is outlined below. The goal is to show that Justify each step.

(a)From the given hypotheses, deduce that and  (b) Suppose Then, by continuity, x’(t) > f(x*,y*)/2 for all large t (say, for t T). Deduce from this that for t > T, where C is some constant.

(c) Conclude from part (b) that contradicting the fact that this limit is the finite number x*. Thus,f(x*,y*) cannot be positive.

(d) Argue similarly that the supposition that f(x*,y*) < 0 also leads to a contradiction; hence, f(x*,y*) must be zero.

(e) In the same manner, argue that (g*,y*) must be zero. Therefore,f(x*,y*) = g(x*,y*) = 0 and (x*,y*) is a critical point

Step-by-Step Solution:
Step 1 of 3

Introduction to Chapter 1:  Difference of Squares: a -b =(a-b)(a+b)  Zero Product Property: ab=0; a, b=0 1.1 Linear Equations are first-degree equations in one variable that contain the equality symbol, “=”. Linear equation in the variable x can be expresses in the standard form, ax+b=c, where a ≠, b ∊ ℝ The domain is the largest set of acceptable input values. Of note, the denominator of a fraction cannot be equal to zero. 1.1.1 Solve ax+b=0, solve for x ax+(b-b)=(0-b) 1. Isolate x by subtracting b from both sides. x/a=-b/a 2. Divide both sides by a x=-b/a 1.1.2 Solve 5x-3=2x+8 -2x -2x 1. Subtract 2x from each side 3x-3=8 +3 +3 2. Ad

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##### ISBN: 9780321747730

Fundamentals of Differential Equations was written by and is associated to the ISBN: 9780321747730. The full step-by-step solution to problem: 30E from chapter: 5.4 was answered by , our top Calculus solution expert on 07/11/17, 04:37AM. The answer to “A proof of Theorem 1, page 268, is outlined below. The goal is to show that Justify each step.(a)From the given hypotheses, deduce that and (b) Suppose Then, by continuity, x’(t) > f(x*,y*)/2 for all large t (say, for t T). Deduce from this that for t > T, where C is some constant.(c) Conclude from part (b) that contradicting the fact that this limit is the finite number x*. Thus,f(x*,y*) cannot be positive.(d) Argue similarly that the supposition that f(x*,y*) < 0 also leads to a contradiction; hence, f(x*,y*) must be zero.(e) In the same manner, argue that (g*,y*) must be zero. Therefore,f(x*,y*) = g(x*,y*) = 0 and (x*,y*) is a critical point” is broken down into a number of easy to follow steps, and 114 words. This textbook survival guide was created for the textbook: Fundamentals of Differential Equations , edition: 8. Since the solution to 30E from 5.4 chapter was answered, more than 296 students have viewed the full step-by-step answer. This full solution covers the following key subjects: Zero, argue, must, deduce, Limit. This expansive textbook survival guide covers 67 chapters, and 2118 solutions.

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