Answer to Question #287204 in Calculus for leony

Question

find the approximate value of ∛127

Answer 1

Let y=x^1/3

Let x=125 and $x+\Delta x=127$

$\Delta x=2$

y=125^1/3=5

$\frac{dy}{dx}=1/3(x)^{-2/3}$

$\Delta y=\frac{x^{-2/3}}{3}\Delta x=\frac{2}={3(5)^2}=0.0266$

$y+\Delta y=5+0.0266=5.0266$