Find the Linearization

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.

Find the local linearization of $\ln{(x)}$ at $x = e^2$ and use it to approximate $\ln{(7.4)}$. Also find the error and percentage error.

Approximate $f(x) = \sqrt[3]{x}$ at $x = 26$