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If lim(xto oo) (1+(a)/(x)-(4)/(x^2))^(2x...

If `lim_(xto oo) (1+(a)/(x)-(4)/(x^2))^(2x)=e^3` , the `a` is equal to

A

2

B

`3/2`

C

`1/2`

D

`2/3`

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Verified by Experts

The correct Answer is:
B
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DISHA PUBLICATION-LIMITS AND DERIVATIVES-Exercise -2 : Concept Applicator
  1. If lim(xto oo) (1+(a)/(x)-(4)/(x^2))^(2x)=e^3 , the a is equal to

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  2. If : f(x){:( =1", ... x is rational"),(=0", ...x is irr...

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  3. For x in R, underset(x to oo)lim ((x-3)/(x+2))^(x)=

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  4. If y=(1+x^((1)/(4)))(1+x^((1)/(2)))(1-x^((1)/(4))), then what is (dy)/...

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  5. If underset(x to 0)lim ((sin n x)[(a-n) nx-tan x])/(x^(2))=0, then the...

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  6. underset(n to oo)lim ((n^(2)-n+1)/(n^(2)-n-1))^(n(n-1))

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  7. If y=1/(1+x^(beta-alpha)+x^(gamma-alpha))+1/(1+x^(alpha-beta)+x^(gamm...

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  8. lim(x->0)((cosx)^(1/2)-(cosx)^(1/3))/(sin^2x) is

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  9. lim(x->0)((cosx)^(1/2)-(cosx)^(1/3))/(sin^2x) is

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  10. Let alpha and beta be the distinct root of ax^(2) + bx + c=0 then ...

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  11. If underset(x to 1)lim (ax^(2)+bx+c)/((x-1)^(2))=2" then "underset(x t...

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  12. Evaluate underset(x to pi/4)lim (1-sin 2x)/(1+cos 4x)

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  13. For the function f(x)=(x^(100))/(100)+(x^(99))/(99)+....x^(2)/2+x+1, f...

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  14. The value of lim(xto0)((4^x-1)^3)/(sin.(x^2)/(4)log(1+3x)),is

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  15. If f(x) + f(y) = f((x+y)/(1-xy)) for all x, y in R (xy ne 1) and under...

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  16. Evaluate underset(xto2)lim(x^(2)-x-2)/(x^(2)-2x-sin(x-2)).

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  17. underset(n to oo)lim {1/(1-n^(2))+(2)/(1-n^(2))+....+(n)/(1-n^(2))} is...

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  18. If zr=cos(pialpha)/(n^2)+isin(ralpha)/(n^2), where r=1,2,3....,n, then...

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  19. If f(x)={{:(,|x|+1, x lt 0),(, 0,x=0),(,|x|-1, x gt 0):}" then "unders...

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  20. The value of underset(theta to -pi/4)lim (cos theta +sin theta)/(theta...

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  21. Let f(2)=4 and f'(2)=4. Then lim(x->2)(xf(2)-2f(x))/(x-2) is equal to

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