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value of underset(nrarrinfty)lim((n !)/n...

value of `underset(nrarrinfty)lim((n !)/n^n)^(1/n),where n inN` is equal to

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CENGAGE PUBLICATION-INTEGRALS-All Questions
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  2. Evaluate the following limit: lim(nto oo)(sum(r=1)^(n) sqrt(r)sum(r=...

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  3. value of underset(nrarrinfty)lim((n !)/n^n)^(1/n),where n inN is equal...

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  4. If the value of the definite integral int0^1 "^(207)C7x^(200)(1-x)^7dx...

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  5. Evaluate: int(-1)^0(dx)/(x^2+2x+2)

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  6. If fa n dg are continuous function on [0,a] satisfying f(x)=f(a-x)a ...

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  7. If f(x)=min(|x|,1-|x|,1/4)AAx in R , then find the value of int(-1)^1...

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  8. Evaluate: int0^pie^(|cosx|)(2sin(1/2cosx)+3cos(1/2cosx))sinxdxdot

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  9. Evaluate: inta^b x^3dx

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  10. Find the value of int(-pi/3)^(pi/3)(pi+4x^3)/(2-cos(|x|+pi/3))dx

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  11. Evaluate: ("lim")(n rarr oo)(1/(sqrt(4n^2-1))+1/(sqrt(4n^2-2^2))++1/(s...

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  12. If y(x)=int(pi^2/16)^(x^2)(cosxcossqrt(theta))/(1+sin^2sqrt(theta))d t...

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  13. Evaluate: underset(nrarrinfty)lim[(1/n^2sec^2(1/(n^2))+2/n^2sec^2((4)/...

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  14. For x >0,l e tf(x)=int1^x(logt)/(1+t)dtdot Find the function f(x)+f(1/...

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  15. Evaluate ("lim")(n rarr oo)sum(k=1)^nk/(n^2+k^2)

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  16. If" f, is a continuous function with int0^x f(t) dt->oo as |x|->ooth...

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  17. Show that : pi/6leint0^1dx/sqrt(4-x^2-x^3)lepi/(4sqrt2)

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  18. Let f:[-1,2]->[0,oo) be a continuous function such that f(x)=f(1-x)fo...

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  19. Prove that int0^x e^(x t-t^2) dt=e^(x^(2)/4)int0^x e^-(t^(2)/4)dt

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  20. If alpha=int0^1(e^(9x+3tan^-1x))((12+9x^2)/(1+x^2))dx where tan^-1x t...

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