Linear Approximation Practice Problems

Find the linearization of $f(x) = {(1 + x)}^{P}$ at $0$, and approximate $f(\sqrt{0.99})$

Suppose that a spherical container has a radius of $1 \pm 0.001 m$. Approximate the corresponding possible error in the calculated volume.

Use linear approximations to estimate $\sqrt{8}$. Also find the error and percentage error.

Let $f(x) = \sqrt{x}$ at $x = 4$ and $\Delta{x} = 0.02$

Find $dx$, $dy$, $\Delta{y}$