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Question

If f left parenthesis x right parenthesis equals open curly brackets table attributes columnalign left left columnspacing 1em end attributes row cell 1 over x squared minus 1 over x squared      comma x less than 0 end cell row cell sin to the power of negative 1 end exponent left parenthesis x plus b right parenthesis comma      x greater or equal than 0 end cell end table close then at x equals 0 comma space f left parenthesis x right parenthesis space is

  1. continuous if b=0
  2. discontinuous for any real b 
  3. differentiable for b= ±1
  4. non-differentiable for any real b

The correct answer is: continuous if b=0


    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell text  Continuous  end text not stretchy rightwards double arrow 0 equals sin to the power of negative 1 end exponent straight b end cell row cell text  Differentiable  end text end cell row cell space of 2em table attributes columnspacing 1em end attributes row cell not stretchy rightwards double arrow straight f to the power of straight prime open parentheses 0 to the power of minus close parentheses equals straight f to the power of straight prime open parentheses 0 to the power of plus close parentheses not stretchy rightwards double arrow 0 end cell row cell not stretchy rightwards double arrow text  not possible  end text end cell end table not stretchy rightwards double arrow 0 equals 0 end cell end table space

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