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Le t f(x) ={{:((sinpix)/(5x)",",xne0),("...

Le t `f(x) ={{:((sinpix)/(5x)",",xne0),(" "k",",x=0):}` if (x) is continous at `x=0`, then k is equal to

A

`(pi)/(5)`

B

`(5)/(pi)`

C

1

D

0

Text Solution

Verified by Experts

The correct Answer is:
A
Since , f(x) is continuous at `x=0`,
`therefore lim_(xto0)f(x)=f(0)`
`rArr lim_(xto0)(sinpi x)/(5x)=k`
`rArr 1((pi)/(5))=krArr k=(pi)/(5)`
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