Let f (x) = 2 x2 1 , x _= 1, 1 (a) Show that lim x+ f (x) = 0 and lim x f (x) = 0 That

Chapter 5, Problem 36

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Let f (x) = 2 x2 1 , x _= 1, 1 (a) Show that lim x+ f (x) = 0 and lim x f (x) = 0 That is, show that y = 0 is a horizontal asymptote of f (x). (b) Show that lim x1 f (x) = and lim x1+ f (x) = + and that lim x1 f (x) = + and lim x1+ f (x) = That is, show that x = 1 and x = 1 are vertical asymptotes of f (x). (c) Determine where f (x) is increasing and where it is decreasing. Does f (x) have local extrema? (d) Determine where f (x) is concave up and where it is concave down. Does f (x) have inflection points? (e) Sketch the graph of f (x) together with its asymptotes.