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lim [1(1/sin^2(x))+2^(1/sin^2(x))+ x-->0 …..+n^(1/sin^2(x))]^sin^(x)

lim    [1(1/sin^2(x))+2^(1/sin^2(x))+     x-->0      …..+n^(1/sin^2(x))]^sin^(x)                                                                                                                                                                                                                                                                     
 

Grade:11

1 Answers

Nishant Vora IIT Patna
askIITians Faculty 2467 Points
4 years ago
It is 1^infi form

hence the method to be applied is

Lim x-->0 {1^ cosec^2x + 2^cosec^2 x + ….......... n^ cosec^2 x}^ sin^2 x

hence e^Lim x-->0 {1^ cosec^2x + 2^cosec^2 x + ….......... n^ cosec^2 x – 1 }sin^2 x

hence e^Lim x-->0 n^ cosec^2 x {1/n^ cosec^2x + 2/n^cosec^2 x + ….......... 1^ cosec^2 x – 1 }sin^2 x

= n

hence ans is n

Thanks

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