Curve Sketching Example

The previous post was in desperate need of an example! Here is a fully fleshed out problem using the recipe from the previous posting.

If you need art tutoring I guess we can help with that too!

Curve Sketching

Being able to sketch the graph of a function is an important skill to hone. With the tools of calculus you can get a great deal of information about the geometry of a function, so you don't have to spend an eternity plotting an uncountable number of points! By this reasoning the following general tips could actually save your life. Examples to follow, check back soon.

Looks brutal but you essentially use the same tool repeatedly. 

Product rule with many functions

Here is a little write up on the product rule. It shows how to extend to the product of several functions.
So next time you see the function y = x sin(x) ln(x) erf(x) at work you won't be too afraid of its tangents!

Squeeze Theorem Example

Here is a cute example of the squeeze theorem from calculus. This theorem allows you to calculate the limit of a function at a point, supposing you know two other functions that bound said function above and below and both of which share the limit in question. These two auxiliary functions thus "squeeze" your function at the point in question. Here is one with a cool, albeit roughly sketched graph. This was done quickly at the very end of a session so it is not as neat as I would like, please bear with.