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Mathematics 21 Online
OpenStudy (aravindg):

guys anyone knw limits and continuity??

OpenStudy (nikvist):

:-)

OpenStudy (aravindg):

u knw??

OpenStudy (nikvist):

maybe

OpenStudy (aravindg):

meanss?

OpenStudy (nikvist):

post question

OpenStudy (aravindg):

k

OpenStudy (aravindg):

find limit

OpenStudy (aravindg):

(note dont use el hospital :))

OpenStudy (aravindg):

\[\lim_{? \rightarrow 0} (x ^{3}\cot x)/(1-\cos x)=?\]

OpenStudy (aravindg):

help

OpenStudy (nikvist):

\[\lim_{x\rightarrow 0}\frac{x^3\cot{x}}{1-\cos{x}}=\lim_{x\rightarrow 0}\frac{x^3\cot{x}}{2\sin^2{(x/2)}}=\lim_{x\rightarrow 0}\frac{x^3\cos{x}}{2\sin^2{(x/2)}\sin{x}}=\]\[=\lim_{x\rightarrow 0}\frac{x^3}{2\sin^2{(x/2)}\sin{x}}=\lim_{x\rightarrow 0}\frac{4(x/2)^2x}{2\sin^2{(x/2)}\sin{x}}=\]\[=2\cdot\lim_{x\rightarrow 0}\left(\frac{x/2}{\sin{(x/2)}}\right)^2\cdot \lim_{x\rightarrow 0}\frac{x}{\sin{x}}=2\]

OpenStudy (aravindg):

wow i hav some more do u hav board in twiddler?

OpenStudy (aravindg):

nikvist??

OpenStudy (aravindg):

..........plz reply?

OpenStudy (nikvist):

no I haven't got

OpenStudy (aravindg):

oh here its take long time to get answers done :) u see i hav tons of work to do?can u help a bit??

OpenStudy (aravindg):

i am a great fan of u!!

OpenStudy (nikvist):

send to my mail if you want?

OpenStudy (aravindg):

wow thx a lot!!!!!!!!!!!!!THANK YOU THANK YOU THANK YOU!!!!!!!1

OpenStudy (aravindg):

whats ur id?

OpenStudy (nikvist):

nikvist@gmail.com

OpenStudy (aravindg):

i sent a test mail u got it?

OpenStudy (aravindg):

....

OpenStudy (nikvist):

ok

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