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If lim(xto0)({(a-n)nx-tanx}sin nx)/(x^(2...

If `lim_(xto0)({(a-n)nx-tanx}sin nx)/(x^(2))=0`, where `n` is non zero real number then a is equal to

A

0

B

`(n+1)/(n)`

C

`n`

D

`n+(1)/(n)`

Text Solution

Verified by Experts

The correct Answer is:
D
We have,
`lim_(xto0){((a-n)nx)/(x)-(tanx)/(x)}(sinnx )/(x)=0`
` rArr lim_(xto0)n{(a-n)n-(tanx)/(x)}(sinnx)/(nx)=0`
` rArr n[(a-n)n-1]=0`
`rArr (a-n)n=1rArr a=n+(1)/(n)`
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