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Consider the function f(x)={{:((sin2x)...

Consider the function
`f(x)={{:((sin2x)/(5x),if ,xne0),((2)/(15),if,x=0):}`
Which one of the following is correct in respect of the function?

A

It is not continuous at x=0

B

It is continuous at every x

C

It is not continuous at `x=pi`

D

It is continuous at x=0

Text Solution

Verified by Experts

The correct Answer is:
A
`underset(xto0)lim(sin(2x))/(5x)=underset(xto0)lim(sin(2x)(2))/(5.(2x))=(2)/(5)`
But at `x=0,f(x)=(2)/(15)`
Hence, f(x) is not continuous at x=0.
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