Differentials Calculus

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.

Given a circle with a circumference of 56 inches with an error of $\pm{1.2}$ inches. Find the percent error of the area of the circle.