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If f(x)= cases + [x] x , & x 0 2, & x=0 + [ x-x x^3 ], & x 0 cases (where [.] denotes the greatest integer function) if f ( x ) is continuous at x=0 , then is equal to

Options

  1. A-1
  2. B+1
  3. C+2
  4. D-2

Correct answer

B. +1

Step-by-step solution

aligned & f (0⁺ )= as [x]=0 as x 0⁺ & f(0)= -1 as x-x x^3 =- 1 6 + x 4! + x^2 5 ! + . . & f(0)=2 =2 ; =3 aligned

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