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Evaluate lim(xto0)(1+tan^(2)sqrt(x))^(1/...

Evaluate `lim_(xto0)(1+tan^(2)sqrt(x))^(1/(2x))`

A

e

B

`e^(1//2)`

C

`e^(1//4)`

D

`e^(-1//2)`

Text Solution

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The correct Answer is:
B
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MCGROW HILL PUBLICATION-LIMITS AND CONTINUITY-Exercise (Level 1 Single Correct Answer)
  1. The value of lim(x->oo)x[tan^(- 1)((x+1)/(x+2))-tan^(- 1)(x/(x+2))] i...

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  2. Evaluate lim(xto0)(1+tan^(2)sqrt(x))^(1/(2x))

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  3. If f(x) is continuous at x=0, where f(x)=(sin (a+x)-sin (a-x))/(tan (a...

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  4. lim( x to pi//6) (sin(x-pi//6))/(sqrt3//2-cosx) is equal to

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  5. lim(x to pi//2) (cos x)/(root(3)((1-sinx)) is equal to

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  6. If x^(2)+2x^(3)<=x+f(x)<=x^(3)-2x^(3) for value of x near 0 then lim(x...

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  7. If f(x)=(sin^(-1)([x]+x))/"[x]" , [x] ne 0 =0, [x] = 0 where [x] de...

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  8. The function f(x) = [x] cos((2x-1)/2) pi where [ ] denotes the greate...

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  9. Let f(y)="sin" (y-a)/2 "tan" (piy)/(2a), y ne a. The value of f(a) so ...

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  10. Let f(x)=(1+sinx)^"cosec x" , the value of f(0) so that f is a continu...

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  11. Let f(x)={{:(x+1,","x le 1),(3-ax^2,","x gt 1):} The value of a so tha...

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  12. Let f(x)=[x^(2)+1],([x] is the greatest integer less than or equal to ...

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  13. The function y=sqrt(1/2 -"cos"^2 x) is not continuous at

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  14. The number of points at which the function f(x) = 1/(x-[x]) ([.] denot...

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  15. Let f(x)=x, x in Q , f(x)=1-x , x in R ~ Q then f is continuous only a...

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  16. lim(x to 0) (x tan 2x -2x tan x)/((1- cos 2x)^(2)) equal

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  17. Let f(x)=sqrt(1-cos (x-2))/(x-2), x ne 2. The lim(x to 2) f(x)

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  18. The value of f(0) so that the function f(x) = (sqrt(1+x)-(1+x)^(1/3)...

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  19. The set of all points of continuous of fofof, where f(x) = sgn(x) is

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  20. The set of all points of discontinuity of f(x)=(x-1)/(x^3+6x^2+11x+6)

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