Thursday, 27 March 2014

calculus - Prove the limit is sqrte.





How do you show
lim




I know that \lim\limits_{k \to \infty} \left(1+\frac{1}{k}\right)^k=e but I don't know how to apply this.


Answer



Hint: \frac{a^k}{b^k}=\left(\frac ab\right)^k, and in general, \lim_{k\to\infty}\left(1+\frac xk\right)^k=e^x.


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