Simple Limits

Calculus Level 2

$\lim _{ x\rightarrow \infty }{ \left( 1+\frac { 1 }{ x } \right) } ^{ x\quad +\quad 5 }=\quad ?$

\pi

e Infinity

{ e }^{ 5 }

5 5e

1 solution

Aakhyat Singh
Sep 1, 2017

Let there be another variable h, wherein h=1/x =>The question becomes Lim (1+h)^(5+(1/h)) [as h->0] Let y =(1+h)^(5+(1/h)) =>lny=(5+(1/h)) ln(1+h). Find the limit of (5+(1/h)) ln(1+h) using L Hopital Rule. Then y=e^(that value)=Value of limit

Simple Limits

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