[Solution Library] Show that if 0≤ x≤ a and n ∈ N, then 1+(x)/(1!)+...+(x^n)/(n!)≤ e^x≤


Question: Show that if \(0\le x\le a\) and \(n\in N\), then

\[1+\frac{x}{1!}+...+\frac{{{x}^{n}}}{n!}\le {{e}^{x}}\le 1+\frac{x}{1!}+...+\frac{{{x}^{n-1}}}{\left( n-1 \right)!}+\frac{{{e}^{a}}{{x}^{n}}}{n!}\]

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