Show that lim x x pex = 0 for any positive number p. Graph f (x) = x pex , x > 0, for p
Chapter 5, Problem 64(choose chapter or problem)
Show that lim x x pex = 0 for any positive number p. Graph f (x) = x pex , x > 0, for p = 1/2, 1, and 2. Since f (x) = x pex = x p/ex , the limiting behavior (limx x p ex = 0) shows that the exponential function grows faster than any power of x as x .
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