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Let C(n)= int(1//n+1)^(1//n)(tan^(-1)(nx...

Let `C_(n)= int_(1//n+1)^(1//n)(tan^(-1)(nx))/(sin^(-1) (nx)) dx , "then " lim_(n rarr infty) n^(n). C_(n) ` is equal to

A

1

B

0

C

`-1`

D

`(1)/(2)`

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Verified by Experts

The correct Answer is:
D
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ARIHANT MATHS-DEFINITE INTEGRAL-Exercise (Single Option Correct Type Questions)
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  3. Let C(n)= int(1//n+1)^(1//n)(tan^(-1)(nx))/(sin^(-1) (nx)) dx , "then ...

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  5. Iff(x)=e^(g(x))a n dg(x)=int2^x(tdt)/(1+t^4), then find the value of ...

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  6. If a, b and c are real numbers, then the value of underset(trarr0)(lim...

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  10. Let f(x)=int(2)^(x)(dt)/(sqrt(1+t^(4)) and g be the inverse of f. ...

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  11. For f(x) =x^(4) +|x|, let I(1)= int (0)^(pi)f(cos x) dx and I(2)= int(...

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  12. Let f be a positive function. Let I(1)=int(1-k)^(k)x f[x(1-x)]dx , I(...

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  13. Suppose that the quadratic function f(x) = ax^(2) + bx +c is non-negat...

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  14. Let I (a) =int(0)^(pi) ((x)/(a)+ a sin x)^(2) dx where a is positive r...

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  15. The set of value of 'a' which satisfy the equation int0^2(t-log2a)dt...

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  16. lim(x rarr infty) (x^(3) int(-1//x)^(1//x)("In" (1+t^(2)))/(1+e^(t)) d...

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  17. The value of sqrt(pi(int(0)^(2008)x| sinpi x| dx)) is equal to

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  18. lim(n rarr infty) sum(k=1)^(n) (k)/(n^(2)+k^(2)),x gt 0 is equal to

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  19. Let a gt 0 and f(x) is monotonic increase such that f(0)=0 and f(a)=b...

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  20. Evaluate the definite integral: int0^1((xdx)/(1+x))

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