Find the limit of (x+e^(x/8))^(8/x) as x approaches 6

 Exercise

$\lim_{x\to6}\left(\left(x\:+\:e^{\frac{x}{8}}\right)^{\frac{8}{x}}\right)$

 

Evaluate the limit $\lim_{x\to6}\left(\left(x+e^{\frac{x}{8}}\right)^{\frac{8}{x}}\right)$ by replacing all occurrences of $x$ by $6$

$\sqrt[6]{\left(6+\sqrt[8]{\left(e\right)^{6}}\right)^{8}}$

 

Divide $6$ by $8$

$\sqrt[6]{\left(6+\sqrt[4]{\left(e\right)^{3}}\right)^{8}}$

 

Divide $8$ by $6$

$\sqrt[3]{\left(6+\sqrt[4]{\left(e\right)^{3}}\right)^{4}}$

$\sqrt[3]{\left(6+\sqrt[4]{\left(e\right)^{3}}\right)^{4}}$

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