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lim(n to oo) sum(r=1)^(n) {(r^(3))/(r^(...

`lim_(n to oo) sum_(r=1)^(n) {(r^(3))/(r^(4)+n^(4))}` equals

A

log 2

B

`(1)/(2) log 2`

C

`(1)/(3) log 2`

D

`(1)/(4) log 2`

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Verified by Experts

The correct Answer is:
D
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OBJECTIVE RD SHARMA-DEFINITE INTEGRALS-Chapter Test 2
  1. The value of int(0)^(pi) (1)/(5+3cosx)dx, is

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  2. underset(nrarroo)"lim"[sin'(pi)/(n)+sin'(2pi)/(n)+"......"+sin'((n-1))...

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  3. lim(n to oo) sum(r=1)^(n) {(r^(3))/(r^(4)+n^(4))} equals

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  4. lim(n-gtoo)[(1+1/n)(1+2/n)(1+n/n)]^(1/n)

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  5. Evaluate: (lim)(nvecoo)n[1/(n a)+1/(n a+1)+1/(n a+2)++1/(n b)]

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  6. The solution of the equation int(0)^(x) (1)/(xsqrt(2^(2)-1))dx=(pi)/(1...

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  7. Let I(n)=int(0)^(pi//4) tan^(n) x dx, (n gt1 and n in N), then

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  8. If I(m)=int(1)^(x) (log x)^(m)dx satisfies the relation Im = k-lI(m-1...

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  9. If I(m)=int(0)^(oo) e^(-x)x^(n-1)dx, "then" int(0)^(oo) e^(-lambdax) x...

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  10. If I(m,n)=int(0)^(1)x^(m-1) (1-x)^(n-1)dx then

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  11. The total number of extremum(s) of y=int0^(x^2)(t^2-5t+4)/(2+e^t)dt ar...

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  12. The tangent to the curve y=f (x) at the point with abscissa x =1 from ...

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  13. int(-pi)^(pi) (2x(1+ sinx))/(1+ cos^(2))dx is

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  14. The value of the inntegral int(alpha)^(beta) (1)/(sqrt((x-alpha)(beta-...

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  15. The value of the integral int(alpha)^(beta) sqrt((x-alpha)(beta-x))dx,...

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  16. If int(0)^(x^(2)) sqrt(1=t^(2)) dt, then f'(x)n equals

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  17. The value of integral int(1)^(e) (log x)^(3)dx , is

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  18. If int(x^(2))^(x^(4)) sin sqrt(t) dt, f'(x) equals

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  19. lim(n-gtoo)[(1+1/n)(1+2/n)(1+n/n)]^(1/n)

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  20. The value of lim(n->oo) [(1+1/n^2)(1+2^2/n^2)...(1+n^2/n^2)]^(1/n)

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