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
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`
4 views
1 Answers
Correct Answer - 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`
4 views
Answered