Solution: Let f(x)=∑_n=0^∞ (x^n)/(n !). Find the interval of convergence of f. Show that f^prime(x)=f(x). Show that f(0)=1. Identify the function
Question: Let \(f(x)=\sum_{n=0}^{\infty} \frac{x^{n}}{n !}\).
- Find the interval of convergence of \(f\).
- Show that \(f^{\prime}(x)=f(x)\).
- Show that \(f(0)=1\).
- Identify the function \(f\).
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