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lim(x to 0) (1+ sin x)^(1//x^(2)) is equ...

`lim_(x to 0) (1+ sin x)^(1//x^(2))` is equal to:

A

0

B

`infty`

C

`e^(1//2)`

D

does not exist

Text Solution

Verified by Experts

The correct Answer is:
B
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ML KHANNA-LIMITS, CONTINUITY AND DIFFERENTIABILITY -PROBLEM SET (2) (MULTIPLE CHOICE QUESTIONS)
  1. If f(x) is an odd function of x and "lt"(x to 0) f(x) exists then the...

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  2. Lt(x to 0)(e^(1//x)-1)/(e^(1//x)+1) is equal to:

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  3. lim(x to 0) (1+ sin x)^(1//x^(2)) is equal to:

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  4. lim(xto0)(sin[cosx])/(1+[cosx]), ([.] denotes the greatest integer fun...

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  5. The number of points at which the function f(x) = 1/(log|x|) is discon...

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  6. The function f(x) = (log(1+ax)-log(1-bx))/(x) is not defined at x = 0....

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  7. The value of f(0) so that the function f(x) = (log(1+x^(2) tanx)...

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  8. If the function: f(x) = {{:((x^(2)-(A+ 2)x+A)/(x-2), "for", x ne 2),...

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  9. If f(x) =(cos^(2) pix)/(e^(2x) - 2ex), x ne 1/2, the value of f(1/2), ...

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  10. The value of b for which the function f(x) = {{:(5x-4, 0 lt x le 1)...

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  11. if f(x) = {{:(x + lambda, -1 lt x lt 3),(4, x =3),(3x-5, x gt 3):}, is...

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  12. If the function f(x) = {{:((cos x)^(1//x), x ne 0),(=k, x =0):}, is co...

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  13. Let f(x) = {{:((x^(3) + x^(2) -16x +20)/(x-2)^(2), If x ne 2),(=k, If ...

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  14. Let f(x) =(1- tanx)/(4x-pi), x ne pi/4, x in [0, pi/2]. If f(x) is con...

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  15. The value of f(0), so that the function f(x) = (sqrt(a^(2) -ax + x^(...

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  16. The value of f(0), so that the function f(x)=((27-2x)^2-3)/(9-3(243+5x...

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  17. f(x) ={{:((sqrt(1+px)- sqrt(1-px))/x, -1 le x lt 0),((2x+1)/(x-2), 0 l...

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  18. f(x) =(x-1)^(1/(2-x)) is not defined at x = 2. If f(x) is continuous,...

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  19. The function f(x) = {{:(x^(2)//a, 0 le x lt 1),(a, 1 le x lt sqrt(2)),...

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  20. If f(x) = x^(a) log x and f(0) = 0 then the value of alpha for which ...

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