spongythingz

Find the limit as x approaches 0 of,

((1+x)^(1/x)-e)/x

In wolfram alpha, the answer is -e/2, but I'm not sure how that was obtained.

L'Hopital's rule doesn't really apply as (1+x)^(1/x) is such a pain to differentiate.

Any advice/solutions would be greatly appreciated. Thanks!~

I read on a website which had "T" as in "A-K" for ace king but "K-T". I don't know what it means so some help please?

Consider the curve y = e^(-x^2) and we drew a rectangle bound by the curve and the x axis.

Show that the rectangle will have maximum area when the upper right hand side corner is a point of inflexion.

And can you include working out please?

Sorry I don't have a picture and thanks for your help.

I'm 16 and going to take the HSC next year and I want to study derivatives as in such as the risks of call and put options in university. I have 2 questions.

1. What courses should I take

2. What would be the ATAR requirement of those courses

Thanks!

See http://i280.photobucket.com/albums/kk185/InedibleS... for the picture.

I have 4 questions.

1. State the value of f ' (x) at point A

2. Hence state possible equations for the tangent and normal at A

3. Estimate the value of f ' (0)

4. As x approaches plus minus infinity, what can you say about the values of f ' (x)

I already done questions 1 and 2, but I really don't know about 3.

Thanks in advance.

How come some resolved questions, the best answer is chosen by the asker and why other resolved questions the best answer is chosen by voting?

There is a really cool screen at Googleplex displaying searches being done on Google in real time. Does anyone know a feed of this exists and where can you find it?

It's described at http://sitereservation.com/xooglers/index.cfm?entr... and you can see a picture of it at http://www.ethworld.ethz.ch/events/explore/study_t...

A man walks into a bar. He asks for a glass of water, but instead of giving that to him, the barman takes out his gun. The man get a fright but genuinely says thanks and goes away.

Why?