Help with limits problem

[l.yi]

In my BC Calc class we are learning about applications of derivatives, yet this limit problem completely throws me off. I know I am somehow supposed to use a derivative but I just do not know where to go with it. Any help is greatly, greatly appreciated. So far I have taken the first derivative.

Find the value of the limit lim as k approaches infinity (1 + (1/10^k))^10k

My apologies if that seems convoluted. the entire function is raised to the power 10k and only the 10 in the fraction is raised to the k power.

My work:

f '(x) = [10k(1 + (1/10^k))^10k-1](-k*10^-k-1)

Thanks very much!

 

[HallsofIvy]

I'm afraid you have completely misunderstood the problem. I suspect you are given this to lead you to the derivative of \(\displaystyle e^x\) but the problem itself has nothing to do with a derivative. And, in fact, you are not given a function, f, to differentiate! It is asking, simply, for a limit of a sequence. Have you dealt at all with \(\displaystyle e^x\)? In particular, what definition of the number e does your text give?

 

[l.yi]

I'm afraid you have completely misunderstood the problem. I suspect you are given this to lead you to the derivative of \(\displaystyle e^x\) but the problem itself has nothing to do with a derivative. And, in fact, you are not given a function, t, to differentiate! It is asking, simply, for a limit of a sequence. Have you dealt at all with \(\displaystyle e^x\)? In particular, what definition of the number e does your text give?

Oh, I see it now. You are right, we have dealt with this before. So then is the limit e^10^k?