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JEE Main2012MathematicsLimitsActual

If f(x)=3 x¹⁰-7 x^8+5 x^6-21 x^3+3 x^2-7 , then _ 0 f(1- )-f(1) ^3+3 is

Options

  1. A- 53 3
  2. B53 3
  3. C- 55 3
  4. D55 3

Correct answer

B. 53 3

Step-by-step solution

aligned Let f^ (x) & =3 x¹⁰-7 x^8+5 x^6-21 x^3+3 x^2-7 f^ (x) & =30 x^9-56 x^7+30 x^5-63 x^2+6 x f^ (1) & =30-56+30-63+6 & =66-63-56=-53 aligned aligned & Consider _ 0 f(1- )-f(1) ^3+3 & = _ 0 f^ (1- )(-1)-0 3 ^2+3 (By using aligned L'hospital rule) = f^ (1-0)(-1) 3(0)^2+3 = -f^ (1) 3 = 53 3

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