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99 Percentile Qs Bank for JEE MainMathematicsLimits

If f(x)=x ⁻¹ x , then _ x 1 f(x)-f(1) x-1 equals to

Options

  1. A+3 4
  2. B4
  3. C+1 4
  4. D+2 4

Correct answer

D. +2 4

Step-by-step solution

Given, f(x)=x ⁻¹ x then Then, _ x 1 f(x)-f(1) x-1 ( 0 0 . form ) = _ x 1 f^ (x)-0 1 (using L'Hospital rule) aligned & = _ x 1 ( x 1+x^2 + ⁻¹ x ) & = 1 1+1^2 + ⁻¹= 1 2 + 4 & = 2+ 4 or +2 4 aligned

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