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Ift h ev a l u eof("lim")(nvecoo)(n^(-3/...

`Ift h ev a l u eof("lim")_(nvecoo)(n^(-3/2))dotsum_(j=1)^(6n)sqrt(j)i se q u a ltosqrt(N),t h e n` the value of `N/(12)` is __________

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Verified by Experts

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)
  1. Ift h ev a l u eof("lim")(nvecoo)(n^(-3/2))dotsum(j=1)^(6n)sqrt(j)i se...

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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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  5. IfI=int0^((3pi)/5)(1+x)sinx+(1-x)cosx)dx , then value of (sqrt(2)-1)I...

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  6. If int(0)^(100) f(x)dx=7, then sum(r=1)^(100)int(0)^(1)(r-1+x)dx=.

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  7. The value of int0^((3pi)/2)(|tan^(-1)tanx|-|sin^(-1)sinx|)/(|tan^(-1)t...

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  8. L e tf(x)=x^3=(3x^2)/2+x+1/4 Then the value of (int(1/4)^(3/4)f(f(x))...

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  9. The value of int(0)^(1)(tan^(-1)x)/(cot^(-1)(1-x+x^(2))dx is.

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  10. Let f(x) be differentiate function symmetric about x=2, then the value...

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  11. Let f:[0,oo)vecR be a continuous strictly increasing function, such th...

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  12. If f is continuous function and F(x)=int0^x((2t+3)dotintt^2f(u)d u)dt ...

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  13. If the value of the definite integral int0^1(sin^(-1)sqrt(x))/(x^2-x+1...

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  14. about to only mathematics

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  15. Let g(x) be differentiable on R and int(sint)^1x^2g(x)dx=(1-sint), wh...

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  16. If int0^oox^(2n+1)dote^(-xdx)=360 , then the value of n is

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  17. Let f(x) be a derivable function satisfying f(x)=int0^x e^tsin(x-t)dt...

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  18. Let f(x)=1/x^2 int0^x (4t^2-2f'(t))dt then find f'(4)

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  19. If the value of the definite integral int0^1^(2007)C7x^(2000)dot(1-x)^...

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  20. IfIn=int0^1(1-x^5)^n dx ,t h e n(55)/7(I(10))/(I(11))i se q u a lto

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