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(b) Using limits, show that r = -2 and y = r – 8 are linear asymptotes of the graph of f.

(b) Using limits, show that r = -2 and y = r – 8 are linear asymptotes of the graph of f.

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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Please answer (b). Thank you

r* – 4x2 r(x + 8)(x – 2) 8(7x – 4) Given: f(x) = with f'(x) = and f"(x) = (x+ 2)? (r+ 2)³ 3 (r+ 2)4 (a) Find the domain of f and the intercepts of the graph of f. (b) Using limits, show that r = -2 and y = x – 8 are linear asymptotes of the graph of f. (c) Identify the critical numbers of f and the possible points of inflection of the graph of f. (d) Construct a table of signs for f' and f". Specify the following: i. the intervals on which f is increasing or decreasing, and on which the graph of ƒ is concave up or concave down, and ii. the values of r at which f has relative extrema, inflection points, and vertical asymptotes (if any). (e) Sketch the graph of f with emphasis on concavity. Label all the intercept points, relative extremum points, and inflection points with their coordinates. Show the linear asymptotes of the graph of f and label them with their respective equations.
Transcribed Image Text:r* – 4x2 r(x + 8)(x – 2) 8(7x – 4) Given: f(x) = with f'(x) = and f"(x) = (x+ 2)? (r+ 2)³ 3 (r+ 2)4 (a) Find the domain of f and the intercepts of the graph of f. (b) Using limits, show that r = -2 and y = x – 8 are linear asymptotes of the graph of f. (c) Identify the critical numbers of f and the possible points of inflection of the graph of f. (d) Construct a table of signs for f' and f". Specify the following: i. the intervals on which f is increasing or decreasing, and on which the graph of ƒ is concave up or concave down, and ii. the values of r at which f has relative extrema, inflection points, and vertical asymptotes (if any). (e) Sketch the graph of f with emphasis on concavity. Label all the intercept points, relative extremum points, and inflection points with their coordinates. Show the linear asymptotes of the graph of f and label them with their respective equations.
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