Calculus · Grades 11 to 12
Limits
Find the value a function approaches.
The idea
A limit asks what value a function approaches as x gets close to a point. The function does not have to exist at the point itself.
If direct substitution gives 0/0, factor the top and cancel the common factor. Then substitute again.
Worked examples
- How to Find a Limit by Factoring Evaluate the limit of (x^2 - 9)/(x - 3) as x goes to 3. Four steps, the 0/0 case, and the cancel mistakes to avoid.
- How to Use the Power Rule Differentiate f(x) = x^5 with the power rule. Three steps, the exponent rule, and the drop-the-power mistakes to avoid.
- How to Use the Product Rule Differentiate f(x) = x^2(x + 3) with the product rule. Four steps, the u and v labels, and the product mistakes to avoid.
Practice this topic
4 problems with answers.