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(A) Use mathematical induction to prove that for [tex]x\geq0[/tex] and any positive integer [tex]n[/tex].

[tex]e^x\geq1+x+\frac{x^2}{2!}+...+\frac{x^n}{n!}[/tex]

(B) Use part (A) to show that [tex]e>2.7[/tex].

(C) Use part (A) to show that

[tex]\lim_{x\rightarrow\infty} \frac{e^x}{x^k} = \infty[/tex]

for any positive integer [tex]k[/tex].

I thought that I could easily show that e to the x power was greater than 1 and if I could show that it was greater than 1 plus the Riemann sum:

[tex]\sum_{i=1}^n \frac{x^n}{n!}[/tex] then I would have my proof...

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# Homework Help: Proof w/ natural log and Riemann Sum

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