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What is the value of lim(xto0) (sin|x|)/...

What is the value of `lim_(xto0) (sin|x|)/(x)`?

A

1

B

-1

C

`oo`

D

Limit does not exist

Text Solution

Verified by Experts

The correct Answer is:
D
`underset(xto0)lim(sim|x|)/(x)`, LHL is limit when `xlt0`
LHL = `underset(xto0)lim(sim(-x))/(x)=-underset(xto0)lim(sinx)/(x)=-1`
RHL is limit when `xgt0`
`RHL=underset(xto0)lim(sim(x))/(x)=-1`
So, LHL`ne`RHL
Hence, Limit does not exist.
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