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underset(x to 0)lim ((1-cos 2x)(3+cos x)...

`underset(x to 0)lim ((1-cos 2x)(3+cos x))/(x tan 4x)` is equal to

A

2

B

`1/2`

C

4

D

3

Text Solution

Verified by Experts

The correct Answer is:
A
`lim_(x to 0) ((1-cos2x) (3+cos x))/(x tan 4x)=lim_(x to 0) (2(sin^(2)x)(3+cosx))/(x tan 4x)=lim_(x to 0) 2((sin x)/(x))^(2) ((3+cosx))/(4((tan4x)/(4x)))=2.1.((3+1))/(4)=2`
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