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If the value of lim(n to oo) (n^(-3//2))...

If the value of `lim_(n to oo) (n^(-3//2))`. `sum_(j=1)^(6n)sqrt(j)` is equal to `sqrt(N)`, then the value of `N` is________.

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The correct Answer is:
96
`I=lim_(n to oo)( (sqrt(1)+sqrt(2)+sqrt(3)+………..+sqrt(6n))/(nsqrt(n)))`
`=lim_(nto oo) 1/n sum_(r=1)^(6n)sqrt(r/n)=int_(0)^(6)sqrt(x)dx=[2/3x^(3//2)]_(0)^(6)=2/3 . 6sqrt(6)=sqrt(96)`
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CENGAGE-DEFINITE INTEGRATION -Exercise (Numerical)
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  2. (lim)(nvecoo)n/(2^n)int0^2x^n dxe q u a l s

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  3. A continuous real function f satisfies f(2x)=3(f(x)AAx in RdotIfint0...

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  4. Consider the polynomial f(x)=a x^2+b x+cdot If f(0),f(2)=2, then the m...

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