Limits

[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.

[himanshu121]

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

[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

[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?