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BITSAT2024MathematicsLimitsActual

Given a real valued function ' f ' such that f(x)= array cc ^2 x x^2-[x]^2 & for x 0 1 & for x=0 x x & for x 0 array . then

Options

  1. ALHL =1
  2. BRHL = 1
  3. C_ x 0 f(x) exist
  4. D_ x 0 f(x) does not exists

Correct answer

D. _ x 0 f(x) does not exists

Step-by-step solution

_ x 0⁻ f(x)= _ h 0 -h -h = _ h 0 (1-h) (1-h) = 1 _ x 0⁺ f(x)= _ h 0 ^2 h h^2-[h]^2 = _ h 0 ^2 h h^2 =1 _ x 0 f(x) does not exist.

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