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underset(x to 0) lim(x cot(4x))/(sin^(2)...

`underset(x to 0) lim(x cot(4x))/(sin^(2) x cot^(2)(2x))` is equal to

A

4

B

0

C

1

D

2

Text Solution

Verified by Experts

The correct Answer is:
C
`lim _(x to 0) (x cot 4x )/(sin ^(2) cot ^(2) 2x )= lim _(x to 0) ( x cos 4x xx sin ^(2) 2x )/(sin ^(2) x. sin 4x. cos ^(2) 2x )`
`=lim _(x to 0) ( x cos 4x xx sin ^(2) 2x )/(sin ^(2) x.2 sin 2x cos 2x. cos ^(2) 2x )= lim _(x to 0) (x cos 4 x xx cos x )/(sin x xx cos ^(3) x ) =1`
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