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Discuss with Askiitians Tutors> 1) lim x---> 0 sec^-1(sin x/x) ?2) lim x-...

question mark

1) lim x---> 0 sec^-1(sin x/x)
?2) lim x---> 0 sec^-1(x/sinx)
answer both 1) and 2) pleaseee

moidin afsan , 10 Years ago

Grade 11

2 Answers

Rinkoo Gupta

Last Activity: 10 Years ago

(1) lim x->0 sec^-1(sinx/x)

sec^-1(limx->0 sinx/x)

=sec^-1(1)=0

(2) limx->0sec^-1(x/xinx)

=sec^-1(lim x->0 x/xinx)

=sec^-1(1)=0

Thanks & Regards

Rinkoo Gupta

AskIITians Faculty

Arun Kumar

Last Activity: 10 Years ago

Hi

I'll answer only one question for the second make another post.

$\\\lim _{x\to \:0}\left(sec^{-1} \left(\frac{\sin \left(x\right)}{x}\right)\right) \\\mathrm{If\:}f\left(x\right)\mathrm{\:is\:continuous\:around\:}x=g\left(a\right) \\\mathrm{\:and\:}g\left(x\right)\mathrm{\:is\:continuous\:around\:}x=a\mathrm{,\:then} \\\lim _{x\to a}f\left(g\left(x\right)\right)=f\left(\lim _{x\to a}g\left(x\right)\right) \\\lim _{x\to \:0}\left(\frac{\sin \left(x\right)}{x}\right)=1 \\=> sec^{-1} (-1)=0$

Thanks & Regards, Arun Kumar, Btech,IIT Delhi, Askiitians Faculty

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