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

1 Answer
Nico Ekkart
Dec 18, 2014

its #+oo#. (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:
enter image source here

1 < a
enter image source here

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

When #x \to +oo#, the function also keeps rising. The function also goes to #+oo#, thus:

#lim_{x \to +oo} 1.001^x = +oo#

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