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Calculus: Problems and Solutions
http://thecalculusblog.com
Thecalculusblog.com is a place for calculus problems, solutions, and discussion.
Recent Posts
Properties of Log
There are some properties of logarithms that you absolutely must know to get through calculus. Most students shriek or faint when they see a logarithm, but if you learn these simple rules they become much easier to work with. Get a little practice,...
Limits That Don’t Exist
Some functions don’t have a limit as the value of their parameter approaches . Here’s one example: just doesn’t exist. Why is that? Because as increases, keeps oscillating between 1 and -1. It never approaches any one value, ...
Integration by Parts
When we looked at integrating the natural logarithm, we used a little trick: we took the product rule , integrated it to get , and made a clever choice of and to find the integral we wanted. This is called integration by parts, and it’s usu...
Textbook Rental
There’s a new service for students to rent textbooks for the semester: chegg.com. If you’re not planning on using your books later, this might be a good option for you. Check it out! I should mention that if you’re in a science or...
Integrating the Natural Logarithm
You’ll probably see this integral someday: . It looks so simple, and you think, “gee, I probably was supposed to memorize that” or “oh I can do that, it looks so easy.” But then you don’t remember the antiderivati...
Remembering One Trig Identity
We’ve been talking about a way to figure out trig identities without having to just memorize them. Here is how I showed the identity , by just knowing Euler’s formula and some facts on complex numbers. I started off by using Euler’...

