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NDA2015MathematicsDifferentiationActual

If f(x)= 25-x^2 , then what is Lim _ x 1 f(x)-f(1) x-1 equal to ?

Options

  1. A1/5
  2. B1/24
  3. C24
  4. D- 1 24

Correct answer

D. - 1 24

Step-by-step solution

aligned & f(x)= 25-x^2 & f(1)= 24 & _ x 1 f(x)-f(1) x-1 aligned It is 0 0 (undefined condition) so using L'hospital's rule _ x 1 f ^ ( x )-0 1 = _ x 1 ( 25- x ^2 )^ _ x 1 1 2 1 25-x^2 (-2 x)= 1 2 1 25-(1)^2 (-2)=- 1 24

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