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lim(n rarr infty) sum(k=1)^(n) (k)/(n^(...

`lim_(n rarr infty) sum_(k=1)^(n) (k)/(n^(2)+k^(2)),x gt 0 ` is equal to

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ARIHANT MATHS-DEFINITE INTEGRAL-Exercise (Single Option Correct Type Questions)
  1. For f(x) =x^(4) +|x|, let I(1)= int (0)^(pi)f(cos x) dx and I(2)= int(...

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

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

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

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

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

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

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

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

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

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  11. The value of int (0)^(infty)e^-(a^(2)x) dx is equal to

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  12. lim(lamda to 0)(int(0)^(1) (1+x)^(lambda ) dx)^(1//lambda) Is equal t...

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  13. If 2f (x) +f (-x)=(1)/(x) sin (x-(1)/(x)), then the value of int(1//e...

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  14. The value of the definite integral int(0)^(pi//2)sin x sin 2x sin 3x d...

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  15. If f(x) is differentiable function and (f(x).g(x)) is differentiable a...

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  16. The number of integral solutions of the equation 4int (0)^( infty)(log...

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  17. int(0)^(16n^(2)//pi) "cos" (pi)/(2)[(xpi)/(n)] dx is equal to

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  18. If int-2^-1 (ax^2-5)dx=0 and 5 + int1^2 (bx + c) dx = 0, then

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  19. The value of int(3)^(6)(sqrt(x+sqrt(12x-36))+sqrt(x-sqrt(12x- 36)))dx...

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  20. Let In=int(-n)^n({x+1}*{x^2+2}+{x^2+3}{x^2+4})dx, where { } denote the...

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