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:The exponential function f(x) = e x dominates any ”power of x” function as x increases...

:The exponential function f(x) = e x dominates any ”power of x” function as x increases to infinity. That is lim x k e x = 0 for every positive value k. Use the power series given below to verify this fact. e x = 1 + x + x 2 2! + x 3 3! + x 4 4! + x 5 5! + ...

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