Calculus 1: Linear Approximation and Differentials

Let $f(x) = \ln{(x)}$ Find the linearization of $f$ at $1$ and use it to evaluate $\ln{(0.9)}$

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

Find the linearization of $\csc{x}$ at $x = \frac{\pi}{4}$ and use it to approximate $\csc{1}$. 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.