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AP EAMCET202316 May 2023Morning ShiftMathematicsLimitsActual

If f(x)= array ll x (1+ 1 2 ( x^2 ) ), & x 0 0, & x=0 array . , then _ x 0 f(x)-f(0) x

Options

  1. Ais equal to f(0)
  2. Bdoes not exist
  3. Cis equal to 1 2
  4. Dis equal to f (1)

Correct answer

B. does not exist

Step-by-step solution

_ x 0 f(x)-f(0) x = _ x 0 x (1+ 1 2 ( x^2 ) )-0 x = _ x 0 1+ 1 2 ( x^2 )=1+ 1 2 ( _ x 0 x^2 ) _ x 0 x^2 - ( _ x 0 x^2 ) is an oscillatory value between 1 and -1 . _ x 0 f(x)-f(0) x does not exist.

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