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Most Important Selected Qs for JEE AdvancedMathematicsLimits

If _ x f (x^2 )=a (a finite nubmer), then which of the following is/are true

Options

  1. A_ x x^2 f^ (x^2 )=0
  2. B_ x x^2 f^ (x^2 )=2 a
  3. C_ x x^4 f^ (x^2 )=0
  4. D_ x x^4 f⁻ (x^2 )=a

Correct answer

C. _ x x^4 f^ (x^2 )=0

Step-by-step solution

We have _ x f (x^2 )=a _ x x f (x^2 ) x =a Applying L.H. rule we have _ x x^2 f^ (x^2 )=0 Again applying L.H. rule = _ x x^3 f^ (x^2 ) x =0 we get _ x x^4 f^ (x^2 )=0

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