Math question inside!

Question

poofypenguin · Answer

attachment

poofypenguin · Answer

I'm not actually sure how to approach this question...can anyone help me?

hartnn · Answer

can u use L'Hopital's rule ?

poofypenguin · Answer

sure...so i take the derivative of the numerator and denominator?

hartnn · Answer

yup.

hartnn · Answer

do u know how to derivate ln (sinh 5x) ?

poofypenguin · Answer

i think so, is it just by using the chain rule?

hartnn · Answer

yes, chain rule it is...

poofypenguin · Answer

alright! i shall give it a try!

hartnn · Answer

ask if u don't get it....

poofypenguin · Answer

I don't think i've gotten the right answer... i'm typing the answer into a computer system and it says that infinity isn't defined... here's the work that i've done:

hartnn · Answer

write cosh / sinh  as coth 
and coth infity is = 1

poofypenguin · Answer

i'm not sure i understand what you mean by cosh / sinh  as coth? could you please explain?

hartnn · Answer

that is standard identity , like 
$\huge \frac{\cos x}{\sin x}=\cot x,\frac{\cosh x}{\sinh x}=\coth x \ and \: \:\coth \infty=1 $

hartnn · Answer

so, u get coth 5x*coth7x and when u put x=infinity, u get that = 1*1=1

hartnn · Answer

ok ?

poofypenguin · Answer

yeah... i understand what you did...but i typed in 1 as the final answer and it came out incorrect... maybe i did something wrong in my simplification?

hartnn · Answer

and don't forget 5/7

hartnn · Answer

5/7 *1*1 = 5/7

poofypenguin · Answer

Oh! Whoops! i missed that!

poofypenguin · Answer

I got it now! Thanks so much for all of your help! :D

hartnn · Answer

welcome ^_^