# Calculating Rates from the Limit Definition

Students often struggle with calculating rates from the limit definition,

Because of this, there are many FAQs available to help you work through these problems.

These examples should help you to solve problems from Section 11.2 and Section 11.3.

# Another System of Linear Equations

Often the most difficult part of solving a system of equations problem is writing out the system from a word description. In this FAQ, we look at a complicated sounding problem and form a system of linear equations from the problem.

This FAQ explores how to take a story problem and write it out as a system of linear equations.

# Tables and Excel

Excel comes in handy for creating tables of values for limits. This FAQ contains two PDFs that demonstrate the process of creating a table using a “fill” in Excel.

How Do I Make A Table Of Values In Excel?

This same process may be used to create tables in other types of spreadsheets such as Google Sheets.

# Piecewise Functions and Taxes

A terrific example of piecewise functions is our graduated income tax system. In that system, the more you make…the higher percentage you pay. However, you DO NOT pay the higher percentage on all of your income. In the two FAQ’s below,we take a look how all of this works.

This FAQ shows how to take a tax table from the Arizona tax forms and convert it into a piecewise function.

In this FAQ we incorporate the idea that the amount you are taxed depends on the tax bracket you fit in.

This topics comes from Section 1 of Chapter 10 in Applied Calculus and is used in Section 5 of the same chapter.

# How Do I Graph Equations To Find the Rate For A Sinking Fund?

In Section 5.3, you are asked to find the rate in a sinking fund. Using the ordinary annuity formula results in an equation that is very difficult to solve. Instead, try graphing each side to the equation and locating the point of intersection.

Goto the MathFAQ >>