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dinainjune
Group Title
lim┬(x→π/2)〖(π(π2x) tan〖(xπ/2)〗)/(2(xπ) 〖cos〗^2 x)〗
 3 years ago
 3 years ago
dinainjune Group Title
lim┬(x→π/2)〖(π(π2x) tan〖(xπ/2)〗)/(2(xπ) 〖cos〗^2 x)〗
 3 years ago
 3 years ago

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dinainjune Group TitleBest ResponseYou've already chosen the best response.0
this is limit of trygonometry, i put it on the ms.word
 3 years ago

malevolence19 Group TitleBest ResponseYou've already chosen the best response.1
Thats indeterminate (0/0) so you would do l'hospital's rule. Have you done that?
 3 years ago

dinainjune Group TitleBest ResponseYou've already chosen the best response.0
yes, i have done. but, i'm stuck in trygonometry. can you do that?
 3 years ago

malevolence19 Group TitleBest ResponseYou've already chosen the best response.1
The functions involved in the limit are arbitrary as long as they are easily differentiable and the limits actually exist. So taking the derivatives you have: \[\frac{\pi}{2}\lim_{x \rightarrow \frac{\pi}{2}}\frac{(2)(\tan(x\frac{\pi}{2}))+(\pi2x)\sec(x\frac{\pi}{2})\tan(x\frac{\pi}{2})}{\cos^2(x)+(x\pi)(2)(\sin(x))\cos(x))}\] However you notice this is still undeterminate. (0/0) so you have to differentiate it again.
 3 years ago

malevolence19 Group TitleBest ResponseYou've already chosen the best response.1
So differentiate it again: \[\frac{\pi}{2}\lim_{x \rightarrow \frac{\pi}{2}}\frac{2 \pi \csc^3(x) (2 \sin(x)+(\pi2 x) \cos(x))}{4 (\pix) \cos(2 x)4 \sin(2 x)}\] Evaluating this should give you 2.
 3 years ago

dinainjune Group TitleBest ResponseYou've already chosen the best response.0
Thank you
 3 years ago

malevolence19 Group TitleBest ResponseYou've already chosen the best response.1
No problem, sorry its so gross looking :/
 3 years ago

dinainjune Group TitleBest ResponseYou've already chosen the best response.0
it's okay, you help me anyway :)
 3 years ago
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