Represent sinh2x as power series

synergix
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Homework Statement



find the first three non zero terms of a power series representation of f(x)= sinh 2x

Homework Equations



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The Attempt at a Solution



seems easy enough do I just substitute 2x for x?

so sinh 2x= 2x + 8x3/3! + 32x5/5!
 
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Yes that should be correct.
 
Thanks I messed this one up on a test because I forgot to put the formula on my cheat sheet but damn that was easy
 
You didn't really need to have the formula on your cheat sheet if you know how to differentiate sinh(2x). Just use the general formula for a Taylor series.
 
Dick said:
You didn't really need to have the formula on your cheat sheet if you know how to differentiate sinh(2x). Just use the general formula for a Taylor series.

Or if you know how to express sinh(x) in terms of exponentials, and you know the Taylor series for exp(x).
 
Well I tried using Taylor series and am happy to say that was also very easy and much more satisfying. Those Taylor series aren't so bad after all:)
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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