How do I prove sinh x?

**rideorsmurf** · February 24th 2009, 04:53 PM

I need to prove the Maclarin Expansion of $Sinh (x)$ .I know $Sinh (x) = (e^x - e^-x)/2$ but where do go from here? Please Help.

**Grandad** · February 24th 2009, 10:27 PM

Hello rideorsmurf

Originally Posted by rideorsmurf

I need to prove the Maclarin Expansion of $Sinh (x)$ .I know $Sinh (x) = (e^x - e^-x)/2$ but where do go from here? Please Help.

Use the expansions of $e^x$ and $e^{-x}$ :

$e^x = 1 + x + \frac{x^2}{2!}+ \frac{x^3}{3!}+ \frac{x^4}{4!}+ \frac{x^5}{5!}+ \dots$

$e^{-x} = 1 - x + \frac{x^2}{2!}- \frac{x^3}{3!}+ \frac{x^4}{4!}- \frac{x^5}{5!}+ \dots$

... and subtract:

$e^x-e^{-x} = 2x +2\frac{x^3}{3!}+ 2\frac{x^5}{5!}+ \dots$

$\Rightarrow \sinh x =x +\frac{x^3}{3!}+ \frac{x^5}{5!}+ \dots$

Grandad

**rideorsmurf** · February 25th 2009, 07:43 AM

Thank you so much. That was a lot simpler than I was making it out to be.

Thread: How do I prove sinh x?

LinkBack

Thread Tools

Display

How do I prove sinh x?

Sinh x

Similar Math Help Forum Discussions

[SOLVED] | sinh (z) |^2 = sinh^2(x) + sin^2(y)

Prove that |sinh y - sinh x| ≤ (cosh a)|y - x|

Sinh and Skn

sinh(x)

sinh

Search Tags