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Show that ("lim")(nvecoo)(1/(n+1)+1/(n+2...

Show that `("lim")_(nvecoo)(1/(n+1)+1/(n+2)++1/(6n))=log6`

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Show that, lim_(n to oo)((1)/(n + 1)+(1)/(n+2)+…+(1)/(6n))=log 6 .

Show that lim_(n rarr oo)((1)/(n+1)+(1)/(n+2)+...+(1)/(6n))=log6

Show tha , lim_(ntooo) ((1)/( n +1)+(1)/( n +2)+ . . . +(1)/( 6 n))= log 6 .

Evaluate lim_(nrarroo) [1/(n+1) + 1/(n+2) + 1/(n+3) +…+ 1/(2n)]

Evaluate lim_(nrarroo) [1/(n+1) + 1/(n+2) + 1/(n+3) +…+ 1/(2n)]

If the value of lim_(n->oo){1/(n+1)+1/(n+2)+.......+1/(6n)} is 'K' then find value of (K - log_e 6)? .

lim_(nrarroo)(1/(n+1)+1/(n+2)+…….+1/(6n))=kln6 , then find the value of k

If I_n=int_0^(sqrt(3))(dx)/(1+x^n),(n=1,2,3. .), then find the value of ("lim")_(nvecoo)I_ndot (a)0 (b) 1 (c) 2 (d) 1/2

A DAS GUPTA-Definite Integration-EXERCISE
  1. Show that ("lim")(nvecoo)(1/(n+1)+1/(n+2)++1/(6n))=log6

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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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