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Evaluate lim(ntooo) (1)/(n^(2(log(e)n-lo...

Evaluate `lim_(ntooo) (1)/(n^(2(log_(e)n-log_(e)(n-1)))+n)`.

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Verified by Experts

`underset(ntooo)lim(1)/(n^(2(log_(e)n-log_(e)(n-1)))+n)`
`=underset(ntooo)lim(1)/(n^(2)("log"_(e)(n)/(n+1))+n)`
`=underset(ntooo)lim(1)/(n^(2)("log"_(e)(1)/(1+(1)/(n)))+n)`
`=underset(xto0)lim(1)/((1)/(x^(2))("log"_(e)(1)/(1+x))+(1)/(x))`
`=underset(xto0)lim(1)/(-(log_(e)(1+x))/(x^(2))+(1)/(x))`
`=underset(xto0)lim(x^(2))/(x-log_(e)(1+x))`
`=underset(xto0)lim(x^(2))/(x-(x-(x^(2))/(2)))=2`
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CENGAGE-LIMITS-Question Bank
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  9. If the value of lim(x rarr oo) (root(3)(x^(3)+x^(2)-root(3)(x^(3)-x^(2...

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  10. Let f(x) be a polynomial satisfying lim(x rarr oo) (x^(2)f(x))/(2x^(5)...

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  11. Let L(1) = Lim(x rarr 0)(cos(pix)(e^(lambda x)-1)/(pi sin x) and L(2) ...

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  12. If Lim(c rarr 0) (asinc+btanc)/c^(3) = 3/2, find the value of |a+2b|.

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  13. Lim(n rarr oo) (1-1/2^(2))(1-1/3^(2))(1-1/4^(2))…(1-1/n^(2)) equals

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  14. The value of Lim(x rarr 0)(sum(k =1)^(2016){(sinx)/x+2015k})/2016 is [...

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  15. Lim(x rarr oo) (30+4sqrtx+7root(3)(x))/(2+sqrt(4x-7)+root(3)(6x-2) )eq...

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  16. If Lim(x rarr0) ((a sin x + b tan x)/x^(3))= 3/2 then |a+2b| is equal ...

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  17. lim(x rarr 0)(1/(1+n^(2))+2/(1+n^(2))+3/(1+n^(2))+....+n/(1+n^(2))) is...

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  18. Find the value of lim(n rarr oo)sum(k=1)^(n)(k^(2)+k-1)/((k+1)!) .

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  19. If Lim(x rarr 0)(1-cos(1-cos(1-cosx)))/x^(a) is finite then teh maximu...

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  20. The value of Lim(x rarr 0)((tanx)^(1/x)+(1+sinx)^(x)) where x gt0 is e...

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  21. Let f(x) be a differentiable function satisfying f(x+y) = f(x)+f(y) A...

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