Linear Approximation Problems

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

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

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.