Solve Limit Question: f(x)=(1+.01x)^(10/x)

[ffrpg]

Here's a question from calc I (I'm currently in calc III). My cousin needs help with this problem and I'm truly 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.

 

[himanshu121]

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

 

[nille40]

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

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

Nille

 

[himanshu121]

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

 

[sam2]

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