Postage on first class mail in the United States is based on weight. Each ounce is charged according to a table published by the US Postal Service. The FAQ below shows how to take this table and write out a piecewise function P(x), where x is the weight of the letter.
I just saw yesterday that the IRS is starting to receive tax returns for the tax year 2016…YIPPEE! In honor of this auspicious moment, I thought I would add a FAQ about how piecewise functions and taxes are related.
The most difficult part of finding a derivative is evaluating the limit involved in the definition of the derivative at a point. Often there is some algebra and simplifying involved as the example below demonstrates.
Many students struggle with slopes of tangent lines versus slopes of secant lines. In the example below, I find these slopes and use them to compute the equation of a tangent line and the equation of a secant line.
The secant line is the red line to the right that passes through two points on the curve. The tangent line is the green line that just grazes the curve at a point.
Suppose you want to generate a table of values from a formula…perhaps to help evaluate a limit. Google Sheets (or any spreadsheet) can quickly generate the values.