Application of Derivatives

Use differentials to approximate: - Wired Faculty

Question

Use differentials to approximate:
$square root of 26$

Solution

$Take space straight y space equals space square root of straight x comma space space space straight x space equals space 25 comma space space space space dx space equals space δx space equals space 1 space space so space that space straight x space space plus δx space equals space 26 Now comma space space space space straight y space plus space δy space equals space square root of straight x plus δx end root rightwards double arrow space space space space space δy space equals space square root of straight x plus δx end root space minus space square root of straight x space equals space square root of 26 space space minus 5 rightwards double arrow space space space space space space square root of 26 space equals space δy space plus space 5 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space.... left parenthesis 1 right parenthesis Now space δy space is space approximately space equal space to space dy$
$and space space space dy space equals space dy over dx space equals space fraction numerator 1 over denominator 2 square root of straight x end fraction dx space equals space fraction numerator 1 over denominator 2 cross times 5 end fraction cross times 1 space equals space 1 over 10 space equals space 0.1 therefore space space space from space left parenthesis 1 right parenthesis comma space space square root of 26 space equals space 0.1 plus 5 space equals space 5.01.$

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Application Of Derivatives

Use differentials to approximate:
$square root of 26$

Some More Questions From Application of Derivatives Chapter

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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