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What is lim(xto0) (sin2x+4x)/(2x+sin4x) ...

What is `lim_(xto0) (sin2x+4x)/(2x+sin4x)` equal to ?

A

0

B

`(1)/(2)`

C

1

D

2

Text Solution

Verified by Experts

The correct Answer is:
C
`underset(xto0)lim(sin2x+4x)/(2x+sin4x)=underset(xto0)lim((sin2x)/(x)+4)/(2+(sin4x)/(x))`
`=underset(xto0)lim(2((sin2x)/(2x))+4)/(2+4((sin4x)/(4x)))`
Applying limit, we get `(2+4)/(2+4)=1`
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