Question

derivative of:

Answer 1

\[(e^x-e ^{-x})\div2\]

Answer 2

well do chain rule....

Answer 3

I suppose that you know what the function actually is, right?

Answer 4

sinhx

Answer 5

so its coshx

Answer 6

Yes. The derivative is really easy. Why were you having trouble?

Answer 7

because then i have to integrate this: \[\int\limits_{0}^{2}\sqrt{1+\cosh^2x}dx\]

Answer 8

Ah, well, see, you know that's not very integrable, right?

Answer 9

Are you sure it's not -cosh^2 x? That would be possible...

Answer 10

no its + finding length of a curve

Answer 11

Oh! okay then! Are you sure your question was not asking for a numerical answer? Was it an AP calc BC problem?

Answer 12

BC, and yes i need a numerical answer.... is it ridiculously easy?

Answer 13

Haha! Yes! You use a calculator!

Answer 14

i need to show work!

Answer 15

i know how to use a calculator

Answer 16

I know! I took BC a while ago. They only expect you to set up the integral on the calculator portion of the exam, and then you write the answer to a thousandth (round or truncate)

Answer 17

well that is stupid. sorry but it is. Thanks!

Answer 18

Why? If it's the calculator part of the exam, I would argue it's stupid to try and integrate that! Also, they just need to check your knowledge of arc length, not hyperbolics and their integrals.

Answer 19

its a homework problem

Answer 20

What does the question say, word for word?

Answer 21

compute the length of the curve f(x) (above function) for \[0\le x \le 2\]

Answer 22

Does it not give any hint at whether it's calculator or not? Either way, it's badly worded. Don't worry about this showing up on the ap. It would be in the calculator section.

Answer 23

here are the lesson instructions: Generally speaking, arc length and surface area integrals are difficult to compute exactly since the integrands often do not have an antiderivative in terms of common functions. So approximation methods are used (such as Trapezoidal Rule) to get an estimate of the integral. But, for all the problems below, the functions have been selected so that the integrals can be done exactly.

Answer 24

I seem to remember that someone had this exact problem. But seriously though, if Wolfram can't solve it, no one can... Anyway, here's a path I'm taking right now:
\[\sqrt{1+(\frac{e^x-e^{-x}}{2})^2}=\frac{1}{2}\sqrt{4+e^{2x}+2+e^{-2x}}\]... Which you can see still leads us nowhere...

Answer 25

yeah. I will just do the calculator version..... works much better :)