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Evaluate, lim(xto0) (sinx-2sin3x+sin5x)/...

Evaluate, `lim_(xto0) (sinx-2sin3x+sin5x)/(x)`

A

`0`

B

`1`

C

`2`

D

`3`

Text Solution

Verified by Experts

The correct Answer is:
A
Given, `=underset(xto0)"lim"(sin5x+sinx-2sin3x)/(x)`
`=underset(xto0)"lim"(2sin3xcos2x-2sin3x)/(x)=underset(xto0)"lim"(2sin3x(cos2x-1))/(x)`
`=underset(xto0)"lim"(2sin3x)/(1/3 xx 3x)(cos2x-1)=6underset(xto0)"lim"(sin3x)/(3x)(cos2x-1)`
`=6underset(xto0)"lim"(sin3x)/(3x).underset(xto0)"lim"(cos2x-1)=6 xx 1 xx 0=0`
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