Application of Derivatives

Use differentials to approximate: - Wired Faculty

Question

Use differentials to approximate:
$square root of 49.7 end root$

Solution

$Take space straight y equals space square root of straight x space space comma space space space space straight x space equals space 49 comma space space space space space dx space equals space δx space equals space 0.7 space space space so space that space straight x space space plus δx space equals space 49.7$
$Now space space space space straight y space plus space δy space equals space square root of straight x plus δx end root space space space space space space space space space space space space space space space space space space rightwards double arrow space space space space space δy space equals space square root of straight x plus δx end root space minus space straight y space equals space square root of 49.7 end root space minus space 7$
$rightwards double arrow space space space space space square root of 49.7 end root space equals space δy plus 7 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space... left parenthesis 1 right parenthesis$