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Discussion Response Post to: find the limit - by (gaurav)

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Priyesh (1601)

Blazing goIITian

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the ans is e^-1

_{x ][ 0 ]} ( sin x / x ) ^{(sin x / x - sinx )}

first we convert the limit to 1^inf form so

= _{x ][ 0 ]} ( sin x / x ) ^{(1/ (x/sinx - 1))} (dividing the num & denom. of the power by sinx)

= (1 + (sinx/x - 1))^{(1/(sinx/x -1) * (sinx/x -1)/(x/sinx - 1)}

now the limit of the bold part becomes e because (lim x---->0 (1 + x)^1/x = e)

now the lim becomes e^{(lim x--->0 (sinx/x -1)/(x/sinx - 1)}

= e^{(lim x--->0 (-sinx/x))}

= e^-1

hope you understood

cheers

"Imagination is more important than knowledge."

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