# Calculus 1: Linear Approximation and Differentials

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

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.

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.

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

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

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

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.

A 12 by 12 square is produced with an error of $\pm{\frac{1}{64}}$ inches in the length of each side. Find the the percent error in the area of one of these squares.