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Application Of Derivatives

Question
CBSEENMA12035590
Wired Faculty App

Use differentials to approximate:
square root of 401









Solution

Take straight y space equals space square root of straight x comma space space space space straight x space equals space 400 comma space space space space space space dx space equals space δx space equals space 1 space space space so space that space straight x space plus space δx space equals space 401
Now space space space space straight y space plus space δy space equals space square root of straight x plus δx end root rightwards double arrow space space space space space space space δy space equals space square root of straight x plus δx end root space minus space straight y space equals space square root of 401 space minus space 20 rightwards double arrow space space space space space space space square root of 401 space equals space δy space plus space 20 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space... left parenthesis 1 right parenthesis Now space δy space is space approximately space equal space to space dy   
and space dy space equals space dy over dx dx space equals space fraction numerator 1 over denominator 2 square root of straight x end fraction dx space equals space fraction numerator 1 over denominator 2 square root of 400 end fraction left parenthesis 1 right parenthesis space equals space 1 over 40 space equals space 0.025 therefore space space space from space left parenthesis 1 right parenthesis comma space space space square root of 401 space equals space 0.025 plus 20 space equals space 20.025.

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