Question

Find the approximate value of $(1.999{)}^5$

Answer 1

Let x = 2
and $△x=-0.001$
Let $y=x^5$
On differentiating both sides w.r.t. x, we get
$\frac{dy}{dx}=5x^{4}Now,△y=\frac{dy}{dx}.△x=5x^4\times △x=5\times 2^4\times [-0.001]\therefore (1.999{)}^5=y+△y=2^5+(-0.080)=32-0.080=31.920$