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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)={((sin x)/(x)+cos x", for " x gt 0),((4(1-sqrt(1-x)))/(x)", for " x lt 0):}`, then `f(0)=`

A

2

B

-2

C

4

D

None of these

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The correct Answer is:
A
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  4. If f(x)={:{(x+2", if " x le 4),(x+4", if " x gt 4):}, then

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

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

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  9. If f(x)={:{(1-x", for " 0 lt x le 1), ( 1/2 ", for " x=0):}, then in [...

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  10. If f(x)={:{(3x+5", for " 0 le x lt 3),(2x+8", for " 3 le x lt 5),(x+13...

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  11. If f(x)={:{((sinx)/(x)", for " x lt 0),(x+1", for " x ge 0):}, then

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  12. If f(x)={((2x+5)/(x+1)", for " 0 le x lt 2),(4x-5", for " 2 le x le 4)...

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  13. If f(x)={:{((sin2x)/(sqrt(1-cos2x))", for " 0 lt x le pi/2),((cos x)/(...

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  14. If f(x)={:{(x", for " 0 le x lt 1),(2", for " x=1),(x+1", for " 1 lt x...

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  15. If f(x)=(x^(3)+3x+5)/(x^(3)-3x+2) in [0, 5], then f is

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  16. If f(x)=(x+1)/((x-2)(x-5)), then in [4, 6]

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  17. If f(x)=(x+1)/((x-2)(x-5)), then in [0, 1]

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  18. If f(x)={:{(x", for " x ge 0),(x^(2)", for " x lt 0):}, then f is

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  19. If f(x)={:{(x^(2)-4", for " 0 le x le 2),(2x+3", for " 2 lt x le 4),(x...

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  20. If f(x)={((1)/(x+1)", for " 2 le x le 4),((x+1)/(x-3)", for " 4 lt x l...

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