Step by Step Solutions

(Steps Shown) Let f(x)=∑limits_n=0^∞ (x^n)/(n!) Find the interval of convergence of f . Show that f'(x)=f(x) Show that f(0)=1 Identify the function

Question: Let \(f\left( x \right)=\sum\limits_{n=0}^{\infty }{\frac{{{x}^{n}}}{n!}}\)

  1. Find the interval of convergence of f .
  2. Show that \(f'\left( x \right)=f\left( x \right)\)
  3. Show that \(f\left( 0 \right)=1\)
  4. Identify the function f .

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Deliverable: Word Document


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