Question

Let y = 4*sqrtx
Estimate the difference delta y when x = 5 using a linear approximation , given that delta x = 0.3

Answer 1

@TuringTest I forgot my linear approximations.

Answer 2

This is phrased strangely for me, but I assume they want you to do is say for \(x\approx x_0=5\) we have that\[y(x)\approx y(x_0)+y'(x_0)(x-x_0)\implies y(x)-y(x_0)\approx y'(x_0)(x-x_0)\]\[\Delta y=y(x)-y(x_0),~~~~\Delta x=x-x_0=0.3\]therefor\[\Delta y\approx y'(5)\Delta x\]

Answer 3

@sam0102493 let me know if that makes sense to you