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If zr=cos(pialpha)/(n^2)+isin(ralpha)/(n...

If `z_r=cos(pialpha)/(n^2)+isin(ralpha)/(n^2),` where `r=1,2,3....,n, then lim_(n->oo) z_1 z_2 z_3...z_n` is equal to

A

`cos alpha +I sin alpha`

B

`cos (alpha//2)-I sin (alpha//2)`

C

`e^(I alpha//2)`

D

`3root(e^(I alpha)`

Text Solution

Verified by Experts

The correct Answer is:
C
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DISHA PUBLICATION-LIMITS AND DERIVATIVES-Exercise -2 : Concept Applicator
  1. Evaluate underset(x to pi/4)lim (1-sin 2x)/(1+cos 4x)

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

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

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

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

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

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

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

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  10. 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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  11. The integer n for which lim(x rarr 0) ((cos x-1) ( cos x - e^x))/x^n i...

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  12. The value f underset(x to pi/2)lim [1^(1//cos^(2)x)+2^(1//cos^(2) x)+....

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  13. The value of underset(x to 2)lim (sqrt(1+sqrt(2+x))-sqrt3)/(x-2) is

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  14. (lim)(xvec0)(sin(picos^2x))/(x^2) is equal to (1) pi/2 (2) 1 (3) ...

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  15. If underset(x to 0)lim (x^(-3) sin 3x+ax^(-2) +b) exists and is equal ...

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  16. If d/(dx)((1+x^4+x^8)/(1+x^2+x^4))=ax^3+bx,then

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

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  18. lim ( x to pi//2 ) ( sec x - tan x ) is equal to

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  19. underset(xto0)lim[(sin(sgn(x)))/((sgn(x)))], where [.] denotes the gre...

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  20. If f(x)=|cos x|, then f' ((3pi)/(4)) is equal to

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