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NDA2021MathematicsLimitsActual

If f(x)= |x| |x| , x 0 , where [.] denotes the greatest integer function, then what is the right-hand limit of f(x) at x=1 ?

Options

  1. A-1
  2. B0
  3. C1
  4. DRight-hand limit of f(x) at x=1 does not exist

Correct answer

C. 1

Step-by-step solution

f(x)= [x] |x| = cases [x] -x , & x 0 [x] x & , x 0 cases Right hand limit of f(x) at x=1 , RHL = _ x 1 [x] x = _ h 0 [1+h] 1+h =1

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