Find the limit of (e/9)^x as x approaches infinity

 Exercise

$\lim_{x\to\infty}\left(\frac{e}{9}\right)^x$

 

Apply the power rule of limits: $\displaystyle{\lim_{x\to a}f(x)^{g(x)} = \lim_{x\to a}f(x)^{\displaystyle\lim_{x\to a}g(x)}}$

${\left(\lim_{x\to\infty }\left(\frac{e}{9}\right)\right)}^{\lim_{x\to\infty }\left(x\right)}$

 

The limit of a constant is just the constant

$\left(\frac{e}{9}\right)^{\lim_{x\to\infty }\left(x\right)}$

 

Evaluate the limit $\lim_{x\to\infty }\left(x\right)$ by replacing all occurrences of $x$ by $\infty $

$\left(\frac{e}{9}\right)^{\infty }$

 

Simplifying

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