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Application Of Derivatives

Question
CBSEENMA12035588
Wired Faculty App

Use differentials to approximate:
square root of 36.3 end root








Solution

Take   straight y space equals space square root of straight x comma space space space space straight x space equals space 36 comma space space space dx space equals space δx equals 0.3 space space space space so space that space space straight x space plus space δx space equals space 36.3
Now,          straight y plus δy space equals space square root of straight x plus δx end root
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 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 36 end fraction left parenthesis 0.3 right parenthesis space equals space fraction numerator 0.3 over denominator 12 end fraction space equals space 0.025 therefore space space space space from space left parenthesis 1 right parenthesis comma space space space space space square root of 36.3 end root space equals space 0.025 plus 6 space equals space 6.025

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The radius of a circle is increasing uniformly at the rate of 4 cm per second Find the rate at which the area of the circle is increasing when the radius is 8 cm.

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