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Let f(x)=lim(nto oo) 1/n((x+1/n)^(2)+(x+...

Let `f(x)=lim_(nto oo) 1/n((x+1/n)^(2)+(x+2/n)^(2)+……….+(x+(n-1)/n)^(2))`
Then the minimum value of `f(x)` is

A

`1//4`

B

`1//6`

C

`1//9`

D

`1//12`

Text Solution

Verified by Experts

The correct Answer is:
D
`f(x)=lim_(nto oo)( 1/n)(x+1/n)^(2)+(x+2/n)^(2)+………+(x+(n-1)/n)^(2)`
`=int_(0)^(1)(x+y)^(2)dy`
`=x^(2)+x+1/3`
`:. f(x)=(x+1/2)^(2)+1/3-1/4`
`:.f(x)|_("min")=1/12`
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