Application of Derivatives

Use differentials to approximate: - Wired Faculty

Question

Use differentials to approximate:
$square root of 51$

Solution

$Take space space space straight y space equals space square root of straight x comma space space space space space space straight x space equals space 49 comma space space space space dx space equals space δx space equals space 2 space space space so space that space straight x space plus space δx space equals space 51$
$Now comma space straight y plus δy space equals space square root of straight x plus δx end root space space space space space space space rightwards double arrow space space space space space δy space equals space square root of straight x plus δx end root space minus space straight y space equals space square root of 51 space minus space 7 space rightwards double arrow space space space space space space square root of 51 space equals space δy space plus space 7 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space... left parenthesis 1 right parenthesis space space space space space space space$