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.
Author: Dr Dave
What is the Difference Between A Secant Line and a Tangent Line?
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.
How Do You Solve A Linear System with WolframAlpha?
Many of you may already be familiar with using a graphing calculator to put a matrix in reduced row echelon form. Did you know that you can do the same thing with WolframAlpha?
To see how this is done, let’s start from the system of linear equations
How Does Elimination Compare to Matrix Elimination?
You probably noticed that the process we used to solve linear systems in Section 2.2 is almost identical to the process we used to solve linear systems in Section 2.4.
To make this concrete, let’s compare the steps for the system
How Do You Model a Stock Portfolio Containing Two Stocks?
Suppose we want to construct a stock portfolio containing two stocks. If we have $50,000 to invest and desire a total dividend return of 3%, how much must we invest in each stock?
Although this is a pretty simple portfolio, it gives us insight into how we can model the portfolio with a system of linear equations.