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If f(x) is continuous at x=0, where f(x...

If `f(x)` is continuous at `x=0`, where `f(x)=((4^(sin x)-1)^(2))/(x log (1+2x))`, for `x!=0`, then `f(0)=`

A

`1/4 (log 4)^(2)`

B

`1/2 (log 4)^(2)`

C

`2 (log 4)^(2)`

D

`2 (log 2)^(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
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NIKITA PUBLICATION-CONTINUITY-MULTIPLE CHOICE QUESTIONS
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  2. If f(x)=((8^(x)-1)^(2))/(sin x log (1+ x/4)) in [-1, 1] - {0}, then f...

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  3. If f(x) is continuous at x=0, where f(x)=((4^(sin x)-1)^(2))/(x log (...

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  4. If f(x) is continuous at x=0, where f(x)=((3^(sin x)-1)^(2))/(x log (...

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  5. If f(x) is continuous at x=0, where f(x)={:{(((e^(x)-1)^(4))/(sin(x^(2...

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  6. If f(x)=(e^(x)+e^(-x)-2)/(x sin x), for x in [(-pi)/(2), (pi)/(2)]-{0}...

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  7. The function defined by f(x)={:{((1+tan^(2)sqrt(x))^((1)/(2x))", for "...

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  8. The function defined by f(x)={((x^(2)+e^((1)/(2-x)))^(-1)",",x ne 2)...

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  9. If f(x)=x^(2)-sin x+5, then at x=pi

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  10. If f(x)={:{(x", for " 0 le x lt 1/2),(1-x", for " 1/2 le x lt 1):} , t...

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  11. If f(x)={:{((x^(2)-9)/(x-3)", for " 0 lt x lt 3),(x+3", for " 3 le x l...

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  12. If f(x)={:{((sin 2x)/(sqrt(1-cos 2x))", for " 0 lt x lt pi/2),((cos x)...

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  13. If f(x)={:{(x-1", for " 1 le x lt 2),(2x+3", for " 2 le x le 3):}, the...

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  14. If f(x)={:{(x sin x", for " 0 lt x le pi/2),(pi/2 sin (pi+x)", for " p...

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  15. If f(x) is continuous at x=0, where f(x)={((sin x)/(x)+cos x", for " ...

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  16. If f(x)={:{(x+2", if " x le 4),(x+4", if " x gt 4):}, then

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  17. If f(x)={:{(2x", if " x lt 2),(2", if " x=2),(x^(2)", if " x gt2):}, t...

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  18. If f(x)={:{(x-1", for " 1 le x lt 2),(2", for " x=2),(2x-3", for " 2 l...

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  19. If f(x)={:{(x^(2)", for " x le 1),(x+3", for " x gt 1):}, then at x=1

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  20. If f(x)=sqrt(x-2), for 2 lt x lt 4, then f(x) is

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