Approximating Functions Near a Specified Point — Taylor Polynomials

Zeroth Approximation — the Constant Approximation

First Approximation — the Linear Approximation

Second Approximation — the Quadratic Approximation

Whirlwind Tour of Summation Notation

Still Better Approximations — Taylor Polynomials

Some Examples

Estimating Change and $\text{De}x\text{,}\backslash De\; x\backslash text\{,\}$ $\text{De}y\backslash De\; y$ Notation

Further Examples

The Error in the Taylor Polynomial Approximations

(Optional) — Derivation of the Error Formulae

Exercises