Let f (x) = x x 1 , x _= 1 (a) Show that lim x f (x) = 1 and lim x+ f (x) = 1 That is
Chapter 5, Problem 35(choose chapter or problem)
Let f (x) = x x 1 , x _= 1 (a) Show that lim x f (x) = 1 and lim x+ f (x) = 1 That is, show that y = 1 is a horizontal asymptote of the curve y = x x1 . (b) Show that lim x1 f (x) = and lim x1+ f (x) = + That is, show that x = 1 is a vertical asymptote of the curve y = x x1 . (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.
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