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AP EAMCET2013MathematicsApplication of Derivatives

The focal length of a mirror is given by 2 f = 1 v - 1 u . In finding the values of u and v , the errors are equal to ' p '. Then, the relative error in f is

Options

  1. Ap 2 ( 1 u + 1 v )
  2. Bp ( 1 u + 1 v )
  3. Cp 2 ( 1 u - 1 v )
  4. Dp ( 1 u - 1 v )

Correct answer

A. p 2 ( 1 u + 1 v )

Step-by-step solution

Given, equation is 2 f = 1 v - 1 u Differentiating the given equation, we have aligned - 2 f^2 d f & =- 1 v^2 d v+ (- 1 u^2 ) d u & =-p ( 1 v - 1 u ) ( 1 v + 1 u ) ( d v v = d u u =p ) & = -2 p f ( 1 v + 1 u ) [using Eq. (i)] d f f & =p ( 1 v + 1 u ) aligned

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