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AP EAMCET2002MathematicsApplication of Derivatives

The approximate value of (1.0002)³⁰⁰⁰ is

Options

  1. A1.2
  2. B1.4
  3. C1.6
  4. D1.8

Correct answer

C. 1.6

Step-by-step solution

Let y=f(x)=x³⁰⁰⁰ here aligned x & =1, x=0.0002 y & =f^ (x)=3000 x²⁹⁹⁹ x y & =(3000)(0.0002)=0.6 f(x+ x) & =y+ y=1+0.6=1.6 aligned

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