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A function f(x) is defined as f(x)={((1-...

A function f(x) is defined as `f(x)={((1-cos3x)/x^2, x ne 0),(b^2+4, x = 0):}` If f(x) is continuous at x=0, then b equals to

A

`+-2/sqrt3`

B

`+-3/sqrt2`

C

`+-1/sqrt2`

D

`+-sqrt3/2`

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The correct Answer is:
C
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PATHFINDER-LIMIT, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. The number of points at which the function f(x)=1/log|x| is discontinu...

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

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  3. A function f(x) is defined as f(x)={((1-cos3x)/x^2, x ne 0),(b^2+4, x ...

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  4. If f(x)={((cosx)^(1/sinx),"for" x ne 0), (k, "for" x = 0):} The value ...

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  5. Points of discontinuities of the function f(x)=4x+7[x]+2log(1+x), wher...

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  6. The function f(x)=|x|atx=0 is:

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  7. g(x)=x|x|theng''(x)

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  8. The function defined by f(x)={((|x-3),, x ge 1), (1/4x^2-3/2x+13/4,, x...

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  9. If f(x)={((x-1)/(2x^2-7x+5), for x ne 1),(-1/3, for x=1):} then f(1)=

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  10. Let h(x)=max{-x,1,x^2} for every real x, then number of points of non-...

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  11. lim(nrarrinfty)(n^ksin^2n!)/(n+1)=0 for

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  12. If f(x)=sin(2pi[pi^2x])/(5+[x^2]) denotes the greatest integer functio...

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  13. If f(x)=|x-25| and g(x)=f(f(x)) then for xgt50, g'(x) is equal to

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  14. Let f(x)=[tan^2x], where [.]denotes the greatest integer function. The...

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  15. If f(x+y)=f(x). f(y) for all x and y and f(5)=2, f'(0)=4, then f '(5) ...

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  16. if f(x)=[sqrt2sinx], where [x] denotes the greatest integer function, ...

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  17. f(x)=[x]+|x-1| then f(x), where [.] denotes greatest integer function)...

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  18. If f(x)={(-x, x le 1),(3+x, x gt1):}, g(x)= {(x^2, x le 1),(2-x,x gt 1...

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  19. If {x} denotes the fractional part of x, then lim(xrarr0)(e^{x}-1)/x i...

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  20. Consider f(x)={(x^2/|x|, x ne 0),(0, x=0):}

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