# How do you find the limit of  [-1/5(1-(1/x)^(4/5)] as x approaches infinity?

May 12, 2017

Remember that ${\lim}_{x \to \infty} \frac{1}{x} = 0$. Answer: $- \frac{1}{5}$

#### Explanation:

Original question: Find ${\lim}_{x \to \infty} \left[- \frac{1}{5} \left(1 - {\left(\frac{1}{x}\right)}^{\frac{4}{5}}\right)\right]$

Note that ${\lim}_{x \to \infty} \frac{1}{x} = 0$

By substituting $x = \infty$ and using the above statement, we see that the original expression becomes:
${\lim}_{x \to \infty} \left[- \frac{1}{5} \left(1 - {0}^{\frac{4}{5}}\right)\right]$
$= {\lim}_{x \to \infty} \left[- \frac{1}{5} \left(1\right)\right]$
$= - \frac{1}{5}$