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Let f, g: R not stretchy rightwards arrow R be two functions defined by f open parentheses x close parentheses equals open curly brackets table row cell x s i n open parentheses fraction numerator 1 over denominator x end fraction close parentheses comma blank end cell row cell 0 blank comma end cell end table table row cell x blank not equal to 0 end cell row cell x equals 0 end cell end table close blankand g(x) = x f(x)
Statement 1: f is a continuous function at x = 0
Statement 2: g is a differentiable function at x = 0

  1. Both statements 1 and 2 are false    
  2. Both Statements 1 and 2 are true    
  3. Statement 1 is true, Statement 2 is false    
  4. Statement 1 is false, Statement 2 is true    

The correct answer is: Both Statements 1 and 2 are true



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