Question

If $y=x^2+4$ and $x$ change from $3$ to $3.1$, then use differential to a approximate change in $y$.

Answer 1

Given, $y=x^2+4$

At $x=3$

$y=(3{)}^2+4=9+4=13$

$\Delta x=3.1-3=0.1$

$\because y=x^2+4$

Diff. w.r.t. x,

$\frac{dy}{dx}=2x$

$\because dy=\left(\frac{dy}{dx}\right)\Delta x$

$\Rightarrow dy=2x.\Delta x$

$\Rightarrow dy=2\times 3\times 0.1$

$\Rightarrow dy=0.6$

Hence, approximate value of change in $y$ is $0.6$.