Slant asymptote The linear function /1x2 = mx + b, for

Chapter 6, Problem 88

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Slant asymptote The linear function /1x2 = mx + b, for finite m _ 0, is a slant asymptote of f 1x2 if lim xS_ 1 f 1x2 - /1x22 = 0. a. Use a graphing utility to make a sketch that shows /1x2 = x is a slant asymptote of f 1x2 = x tanh x. Does f have any other slant asymptotes? b. Provide an intuitive argument showing that f 1x2 = x tanh x behaves like /1x2 = x as x gets large. c. Prove that /1x2 = x is a slant asymptote of f by confirming lim xS_ 1x tanh x - x2 = 0.

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