It's a limit question

1. Jan 14, 2004

ffrpg

Here's a question from calc I (I'm currently in calc III). My cousin needs help with this problem and I'm truely clueless as of how to solve it. It's a limit question. The questions reads, As X approaches 0 what is the limit of f(x)=(1+.01x)^(10/x). I'm guessing something needs to be done with the power (10/x) but I'm not sure quite sure what.

2. Jan 14, 2004

himanshu121

Apply the formula
$$\lim_{x\rightarrow 0}(1+x)^{\frac{1}{x}}=e$$

3. Jan 14, 2004

nille40

$$\lim_{x\rightarrow 0} f(x) = \left(1 + 0.1x\right)^{\frac{10}{x}} = \left[\begin{array}{cc} t = \frac{1}{10x} \\ x = x \rightarrow 0 \Leftrightarrow t \rightarrow \infty \end{array}\right] =$$$$\lim_{t \rightarrow \infty}f(t) = \left(1 + \frac{0.1}{t}\right)^{t} = \ldots$$

Something with $$e$$. If it would have been $$0.1x$$ instead of $$0.01x$$...

Nille

4. Jan 15, 2004

himanshu121

it would be $$e^{\frac{1}{10}}$$

5. Jan 19, 2004

sam2

How about using the Binomial Exapnsion to re-write the expression and then looking at whether you can simplify it when x--> 0?