Help-me-please-Lim-x-0-1-ex-6x-

Question Number 82682 by zainal tanjung last updated on 23/Feb/20

Help me please \dots .!!

\underset{x \to 0}{Lim} {(\frac{1}{ex})}^{6 x} = \dots

Commented by john santu last updated on 23/Feb/20

\lim_{x \to 0} {(1 + \frac{1}{e x} - 1)}^{6 x} = \lim_{x \to 0} {(1 + \frac{1 - e x}{e x})}^{6 x}

= e^{\lim_{x \to 0} (\frac{1 - e x}{e x}) \times 6 x} = e^{\lim_{x \to 0} (\frac{6 x - 6 {e x}^{2}}{e x})}

= e^{\lim_{x \to 0} (\frac{1 - e x}{e})} = e^{\frac{1}{e}} .

Commented by zainal tanjung last updated on 23/Feb/20

\lim_{m \to \infty} {[1 + \frac{m - e}{e}]}^{\frac{6}{m}}

\lim_{m \to \infty} {[{(1 + \frac{1}{(\frac{e}{m - e})})}^{[\frac{e}{m - e}]}]}^{[\frac{m - e}{e}] (\frac{6}{m})}

e^{\lim_{m \to \infty} [\frac{6 m - 6 e}{me}]} = e^{\frac{6}{e}} = \sqrt[e]{e^{6}}

Commented by john santu last updated on 24/Feb/20

m ? w h e r e y o u g o t m ?