# What is the limit of (1+(a/x) as x approaches infinity?

May 22, 2018

${\lim}_{x \to \infty} \left(1 + \frac{a}{x}\right) = 1$

#### Explanation:

${\lim}_{x \to \infty} \left(1 + \frac{a}{x}\right) = 1 + {\lim}_{x \to \infty} \frac{a}{x}$

Now, for all finite $a , {\lim}_{x \to \infty} \frac{a}{x} = 0$

Hence, ${\lim}_{x \to \infty} \left(1 + \frac{a}{x}\right) = 1$