underset(x to 0)"Lt" x^(2) sin (pi//x)=...

`underset(x to 0)"Lt" x^(2) sin (pi//x)=`

A

1

B

0

C

does not exist

D

`oo`

Text Solution

Verified by Experts

The correct Answer is:

B

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AAKASH SERIES-LIMITS-EXERCISE-II

underset(x to oo)"Lt"sqrt [({x-sin x})/(x+cos^(2)(x))]=
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underset(x to oo)lim {sin sqrt(x+1)-sin sqrtx)=
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underset(x to 0)"Lt" x^(2) sin (pi//x)=
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Lt(x to (pi)/(2)) (sin x)^(tanx)=
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Lt(x to 0)(e^(2x)+x)^(1//x)=
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Lt(x to 1)(log(5)5x)^(log(x)5)=
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Lt(x to a)((sinx)/(sina))^((1)/(x-a))=
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Lt(x to0) ((x)/(sinx))^((cosx)/("x cosec"x-1)=
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lim(xrarr0)[tan(x+(pi)/(4))]^(1//x) is equal to
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Lt(x to 0)(cos((x)/(n)))^(n^(2))=
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Lt(x to oo) ((x^(2)+x+3)/(x^(2)-x+2))^(x)=
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Lt(x to oo) ((x+h)/(x-h))^(x)=4 then h=
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If Lt(x to0) (1+ax)^(b//x)=e^(4), where 'a' and 'b'a re different nati...
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If Lim(x to0) [1+x+(f(x))/(x)]^(1//x)=e^(3), then f(x) is
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underset(x to 0)"Lt" ((1^(x)+2^(x)+3^(x)+....+n^(x))/(n))^(1//x))
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Lt(x to 0) ((2^(x)+2^(2x)+2^(3x))/(3))^(1//x)=
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Lt(x to oo) ((a(1)^((1)/(x))+a(1)^((1)/(x))+....+a(n)^((1)/(x)))/(n))(...
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Lt(x to oo) ((a^((1)/(x))+b^((1)/(x))+c^((1)/(x)))/(3))^(x) when a,b,c...
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Observe the following lists : The correct match is
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Lt(x to0) ((|x|)/(x)+x+2)=
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