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x + 2 x² - 1 (a) On which interval(s) is G(x) > 0? 6. Let G(x): = (b) On which interval(s) is G(x) < 0?

x + 2 x² - 1 (a) On which interval(s) is G(x) > 0? 6. Let G(x): = (b) On which interval(s) is G(x) < 0?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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x + 2 x² (a) On which interval(s) is G(x) > 0? 6. Let G(x) (b) On which interval(s) is G(x) < 0?
Transcribed Image Text:x + 2 x² (a) On which interval(s) is G(x) > 0? 6. Let G(x) (b) On which interval(s) is G(x) < 0?
Expert Solution
Step 1: Find Asymptote

 Given G open parentheses x close parentheses space equals space fraction numerator x plus 2 over denominator x squared minus 1 end fraction

 For obtaining vertical asymptote, equate denominator part equal to zero

                        x squared minus 1 space equals space 0 

             rightwards double arrow      x space equals space plus-or-minus space 1

     x= -1 and x = +1 are two vertical asymptotes. 

similarly for obtaining horizontal asymptote equate numanator part to zero

                     x space plus space 2 space equals space 0  rightwards double arrow  x space equals space minus 2 

   x = -2 is a horizontal asymptote.

                   Using these asymptotes draw graph of G(x) and identify where G(x) is positive and negative


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