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If Sn=[1/(1+sqrt(n))+1/(2+sqrt(2n))+.......

If `S_n=[1/(1+sqrt(n))+1/(2+sqrt(2n))+....+1/(n+sqrt(n^2))]` then `(lim)_(n ->oo)S_n` is equal to (A) `log 2` (B) `log4` (C) `log8` (D) none of these

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CENGAGE PUBLICATION-INTEGRALS-All Questions
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  2. Evaluate: int0^(100)x-[x]dx where [dot] represents the greatest in...

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  3. If Sn=[1/(1+sqrt(n))+1/(2+sqrt(2n))+....+1/(n+sqrt(n^2))] then (lim)(n...

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  4. The value of ("lim")(nvecoo)sum(r=1)^(4n)(sqrt(n))/(sqrt(r)(3sqrt(r)+s...

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  5. The value of (int0^n[x]dx)/(int0^n{x}dx is (where [x] and {x} denotes ...

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  6. Evaluate: int(-pi/4)^(npi-pi/4)|sinx+cosx|dx

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  7. The value of int0^(pi/2)dx/(1+tan^3x) is

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  8. Evaluate: int(-pi)^pi(1-x^2)sinxcos^2xdx

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  9. Let f be a contiuous function on [a,b]. If F(x)=(int(a)^(x)f(t)dt-int(...

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  10. Evaluate the following: int(-1)^(1)(sin x-x^(2))/(3-|x|)dx

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  11. If int(a)^(b)|sinx|dx=8 and int(0)^(a+b)|cosx|dx=9, then find the valu...

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  12. Evaluate: int(-pi/2)^(pi/2)sqrt(cos^(2n-1)x-cos^(2n+1)x)dx ,w h e r en...

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  13. f(x) is a continuous and bijective function on Rdot If AAt in R , the...

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  14. Evaluate: int(-1/2)^(1/2)cosxlog((1-x)/(1+x))dx

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  15. If int0^xf(t) dt=x+intx^1 tf(t)dt, then the value of f(1)

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  16. Evaluate: int0^x[cost]dt where x in (2npi,(4n+1pi/2),n in N ,a n d[do...

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  17. Suppose f is a real-valued differentiable function defined on [1,oo] ...

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  18. Let f be a real valued function satisfying f(x)+f(x+4)=f(x+2)+f(x+6) ...

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  19. If x int(0)^(x)sin(f(t))dx=(x+2)int(0)^(1)tsin(f(t))dt, where xgt0, th...

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  20. Evaluate: int0^2(dx)/((17+8x-4x^2)[e^(6(1-x))+1]

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