# What is the limit as x approaches infinity of 1.001^x?

Dec 18, 2014

its $+ \infty$. (I am assuming you mean $x$ approaches positive infinity)

You can find this simply by looking at the graph of the function. You first have to notice that it's an exponential function (${a}^{x}$). You know this by noticing that there's an $x$ in the exponent. For exponential functions, there are two possible forms.

0 < a < 1:

1 < a

In this case $a = 1.001$, which is bigger than 1
=> The function looks like the second function.

When $x \setminus \to + \infty$, the function also keeps rising. The function also goes to $+ \infty$, thus:

${\lim}_{x \setminus \to + \infty} {1.001}^{x} = + \infty$