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MHT CET202411 May 2024Morning ShiftMathematicsContinuity and DifferentiabilityActual

If f (x)= array cc a 2 (x-|x|), & for x 0 0, & for x=0 b x^2 ( 1 x ), & for x 0 array . is continuous at x=0 , then

Options

  1. Aa is any real value and b is any real value
  2. Ba is only rational value and b is any real value
  3. Ca is only irrational value and b is any real value
  4. Da is only rational value and b is only rational value

Correct answer

A. a is any real value and b is any real value

Step-by-step solution

array ll & _ x 0⁻ f (x)= f (0)= _ x 0⁺ f (x) & _ x 0 a 2 (x-|x|)=0 & _ x 0 a 2 [x-(-x)]=0 [ x 0 |x|=-x] & _ x 0 x=0 array Which is true for any real value of a. _ x 0⁺ f(x)=f(0) limb _ x 0 ~b x^2 ( 1 x )=0 Note that x 0 -1 ( 1 x ) 1 for any real value of b, above limit will be 0.

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