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Find lim(n->oo) Sn ; if Sn=1/(2n)+...

Find `lim_(n->oo) S_n` ; if `S_n=1/(2n)+1/(sqrt(4n^2-1))+1/(sqrt(4n^2-4))+......+1/(sqrt(3n^2+2n-1))`.

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Find lim_(n rarr oo)S_(n); if S_(n)=(1)/(2n)+(1)/(sqrt(4n^(2)-1))+(1)/(sqrt(4n^(2)-4))+......+(1)/(sqrt(3n^(2)+2n-1))

If quad S_(n)=(1)/(2n)+(1)/(sqrt(4n^(2)-1))+(1)/(sqrt(4n^(2)-4))+...+(1)/(sqrt(3n_(2)^(2)+2n-1)),n in N then lim_(n rarr oo)S_(n) is equal to (pi)/(2)(b)2(c)1(d)(pi)/(6),n in N

lim_(n rarr oo)(1)/(sqrt(n^(2)))+(1)/(sqrt(n^(2)+1))+(1)/(sqrt(n^(2) +2))+...(.1)/(sqrt(n^(2)+2n))=

Evaluate: lim_(n rarr oo)((1)/(sqrt(4n^(2)-1))+(1)/(sqrt(4n^(2)-2^(2)))+...+(1)/(sqrt(3n^(2))))

The value of lim_(nto oo)(1/(sqrt(n^(2)))+1/(sqrt(n^(2)+1))+…..+1/(sqrt(n^(2)+2n))) is

li sum_ (n-> oo) sum_ (r = 1) ^ (n) (1) / (sqrt (4n ^ (2) -r ^ (2)))

The value of lim_(n rarr oo)(1/sqrt(4n^(2)-1)+1/sqrt(4n^(2)-4)+...+1/sqrt(4n^(2)-n^(2))) is -

lim_(nto oo)1/n+(1)/(sqrt(n^(2)+n))+(1)/(sqrt(n^(2)+2n))+...(1)/(sqrt(n^(2)+(n-1)n)) is equal to

lim_(nrarroo)((1)/(sqrt(n^(2)))+(1)/(sqrt(n^(2)-1^(2)))+(1)/(sqrt(n^(2)-2^(2)))+....+(1)/(sqrt(n^(2)-(n-1)^(2)))) is equal to

lim_(n rarr oo)(1)/(sqrt(n)sqrt(n+1))+(1)/(sqrt(n)sqrt(n+2))+......+(1)/(sqrt(n)sqrt(4n))

A DAS GUPTA-Definite Integration-EXERCISE
  1. Find lim(n->oo) Sn ; if Sn=1/(2n)+1/(sqrt(4n^2-1))+1/(sqrt(4n^2-...

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  2. Integrate from the first principles int0^(pi/2) sinx dx

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  3. int0^(pi/4)cos^2x dx

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  4. Evaluate int(0)^(1)x^(2)dx as the limit of a sum.

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  5. Integrate:int0^1 2^xdx

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  6. Evaluate the following integrals as limit of sum: inta^b e^x dx

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  7. Integrate int1^2x^3dx

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  8. lim(n to oo)((1)/(1+n^(3))+(4)/(8+n^(3))+....+(r^(2))/(r^(3)+n^(3))+.....

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  9. Evaluate lim(nrarroo)(2)/(n)(sin.(pi)/(2n)+sin.(2pi)/(2n)+sin.(3pi)/...

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  10. underset(ntoinfty)lim(n/(n^2+1^2)+n/(n^2+2^2)+n/(n^2+3^2)+...+1/(2n)) ...

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  11. lim(n rarr oo)[(e^(1//n)+e^(2//n)+e^(3//n)+...+e^(n //n))/n]

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  12. lim(nrarroo)((1)/(sqrt(n^(2)))+(1)/(sqrt(n^(2)-1^(2)))+(1)/(sqrt(n^(2)...

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  13. underset(nto oo)lim{(1)/(n+1)+(1)/(n+2)+(1)/(n+3)+...+(1)/(n+n)} is, e...

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  14. lim(n->oo)1/n[1/(n+1)+2/(n+2)+....+(3 n)/(4 n)]

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

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  16. lim(n->oo)[(1+1/n^2)(1+2^2 /n^2)(1+3^2 /n^2)......(1+n^2 / n^2)]^(1/n)

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  17. Evaluate intcos^5(x/2)sinxdx

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  18. Evaluate the following:int0^(pi/2)(sinxcosxdx)/((a^2cos^2x+b^2sin^2x)^...

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  19. Evaluate int0^(pi//2)(sin^2xdotcos^2x)/((sin^3x+cos^3x)^2)dx

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  20. Evaluate the following:int0^1xlogxdx

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  21. Evaluate : int1^16tan^(- 1)sqrt(sqrt(x)-1)dx

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