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Calculus: Problems and Solutions

Calculus: Problems and Solutions

http://thecalculusblog.com

Thecalculusblog.com is a place for calculus problems, solutions, and discussion.

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  • Properties of Log

    Posted on Wednesday September 16th, 2009 at 13:05 in calculus

    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

    Posted on Friday September 11th, 2009 at 13:05 in calculus

    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

    Posted on Wednesday August 5th, 2009 at 08:55 in integration, calculus, integration by parts, product rule

    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

    Posted on Monday August 3rd, 2009 at 13:54 in calculus

    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

    Posted on Monday July 20th, 2009 at 08:17 in integration, calculus, ln, integration by parts

    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

    Posted on Friday July 17th, 2009 at 16:15 in identities, calculus, trig, complex numbers

    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’...

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