A one-sided limit is a type of limit in calculus that focuses on the behavior of a function as the input approaches a specific value from either the left or the right side. It is also known as a lateral limit.
To calculate a one-sided limit, you need to evaluate the function at values that are approaching the desired input value from only one direction. This means taking the limit as x approaches the input value from either the left or the right side.
The main difference between a one-sided limit and a two-sided limit is the direction of approach. A one-sided limit only considers the behavior of the function as the input approaches from one direction, whereas a two-sided limit takes into account both the left and right side approaches.
Studying one-sided limits is important because it helps us understand the behavior of a function at specific points. It can also help us determine if a function is continuous at a certain point, which is a fundamental concept in calculus and other areas of mathematics.
You can teach yourself about one-sided limits by first understanding the basic concepts of limits and continuity in calculus. Then, you can practice solving problems involving one-sided limits and familiarize yourself with common types of functions that exhibit specific behaviors at certain points. Online resources, such as videos and practice exercises, can also be helpful in learning more about one-sided limits.