Lazy Limits 4!

Calculus Level 3

$\large L= \displaystyle\large \lim_{n\to\infty}{( e^{n\pi}+\pi^{en})}^{1/n} = \, ?$

\pi^{\pi/e}

e^e

e^{\pi/e}

\pi^{\pi}

e^{\pi}

1 solution

Sabhrant Sachan
Jul 9, 2016

$\text{Since } e^{\pi} > \pi^{e} \\ L = \displaystyle\lim_{n \to \infty}\left( e^{\pi n}+{\pi}^{en} \right)^{\frac{1}{n}} \implies e^{\pi}\left(1+\left(\dfrac{{\pi}^{e}}{e^{\pi}}\right)^{n} \right)^{\frac{1}{n}} \\ \boxed{ L = e^{\pi}}$

Lazy Limits 4!

1 solution

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