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underset(x to 0)(lim) ("sin"2X)/(2 - sqr...

`underset(x to 0)(lim) ("sin"2X)/(2 - sqrt(4 - x))` is

A

2

B

4

C

8

D

0

Text Solution

Verified by Experts

The correct Answer is:
C
`lim_(x to 0) (sin 2x)/(2-sqrt(4-x)) xx ((2xxsqrt(4-x)))/((2+sqrt(4-x)))`
`rArr lim_(x to 0) (sin 2x xx (2+sqrt(4-x)))/((4-4+x)) rArr lim_( x to 0) (sin 2x xx (2+sqrt(4-x)))/((2x)/(2)) rArr lim_(x to 0) (2xx sqrt(4-x))/((1)/(2))`
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