Question

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

Answer 1

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:

1 < a

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`