Mark M. answered • 12/15/17

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Retired math prof. Calc 1, 2 and AP Calculus tutoring experience.

The series ∑

_{(n=0 to ∞)}[x^{n}/n!] is the Maclaurin series for e^{x}and has interval of convergence ∞.So, f(x) = e

^{x}.f(0) = e

^{0}= 1f(1) = e

^{1}= ef'(x) = e

^{x}= f(x)f"(x) = e

^{x}= f(x)Mark M.

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^{0}is an indeterminate form. We can't say that 0^{0}is equal to 1 necessarily/
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01/17/18

Imtiazur S.

^{0}01/17/18