How to Change Unacceptable Forms before Using L'Hôpital’s Rule
You can use L'Hôpital’s rule to find a limit for which direct substitution doesn't work. If substitution produces one of the unacceptable forms, ± ∞ · 0 or ∞ – ∞, you first have to tweak the problem to [more…]
How to Solve Limits by Conjugate Multiplication
To solve certain limit problems, you’ll need the conjugate multiplication technique. When substitution doesn’t work in the original function — usually because of a hole in the function — you can use conjugate [more…]
How to Solve Limits at Infinity by Using Horizontal Asymptotes
Horizontal asymptotes and limits at infinity always go hand in hand. You can’t have one without the other. If you’ve got a rational function like [more…]
How to Use Limits to Determine Continuity
Here you’ll learn about continuity for a bit, then go on to the connection between continuity and limits, and finally move on to the formal definition of continuity. [more…]
Solving Easy Limits
There are two types of easy limit problems: the ones you should just memorize and the ones where you can plug in the x-number and get the answer in one step. [more…]
How to Solve Limits with a Calculator
You can solve most limit problems by using your calculator. There are two basic methods. For example, say you want to evaluate the following limit: [more…]
How to Solve Limits by Factoring
You can use the algebraic technique of factoring to solve “real” limit problems. All algebraic methods involve the same basic idea. When substitution doesn’t work in the original function — usually because [more…]
How to Solve Limits with Basic Algebra
When substitution doesn’t work in the original limit function — usually because of a hole in the function — you can often use some algebra to manipulate the function until substitution does work [more…]
How to Solve Limits at Infinity with a Calculator
Solving for limits at infinity is easy to do when you use a calculator. For example, enter the below function in your calculator's graphing mode: [more…]
How to Solve Limits at Infinity by Using Algebra
Yes, you can solve a limit at infinity using a calculator, but all things being equal, it’s better to solve the problem algebraically, because then you have a mathematically airtight answer. For example [more…]
How to Calculate Instantaneous Speed with Limits
You can calculate the instantaneous speed of an object using limits. Say that you and your calculus-loving cat are hanging out one day, and you decide to drop a ball out of your second-story window. Here’s [more…]
How to Make Unacceptable Forms Acceptable before Using L'Hôpital’s Rule
You can use L'Hôpital’s rule to find a limit when other methods don’t work. In fact, even if some other method does work, L'Hôpital’s rule is often a good shortcut. If substitution of the limit number [more…]
How to Determine Limits of Sequences with L'Hôpital's Rule
You can use L’Hôpital’s rule to find limits of sequences. L'Hôpital's rule is a great shortcut for when you do limit problems. Here it is: [more…]
How to Use L'Hôpital's Rule to Solve Limit Problems
L’Hôpital’s rule is a great shortcut for doing some limit problems. (And you may need it someday to solve some improper integral problems, and also for some infinite series problems.) [more…]
How to Solve Limits with a Limit Sandwich
When you can't solve a limit by using algebra, try making a limit sandwich. The best way to understand the sandwich, or squeeze, method is by looking at a graph. [more…]
Evaluating Limits in Calculus
The mathematics of limits underlies all of calculus. Limits sort of enable you to zoom in on the graph of a curve — further and further — until it becomes straight. Once it's straight, you can analyze [more…]
