One sided limits. Teaching myself.

In summary, the problem is to find the one-sided limit of (2x^2+x+1)/(x+2) as x approaches 2 from the right. The function is continuous at x=2, so the limit is just the value of the function at that point. The person asking for help is teaching themselves calculus and knows how to find limits but is struggling with one-sided limits. They are asking for assistance.
  • #1
BBrttnybrat
1
0

Homework Statement


the problem, where you want to find the one sided limit is
Lim (2x^2+x+1)/(x+2)
X=>2-


Homework Equations





The Attempt at a Solution


Well i did attempt the problem. All i can think to put as the answer is finite.


I'm basically teaching myself calculus which as you can imagine is all sorts of fun. I know how to find limits, and how to do stuff like that but the one sided limits throw me off. Please help.
 
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  • #2
Hi BBrttnybrat,

The function you gave is continuous at x=2, so the limit is just the value of the function at that point. Did you mean the limit as x -> -2 from the right, i.e. x -> (-2)- ?
 

FAQ: One sided limits. Teaching myself.

What is a one-sided limit?

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.

How do I calculate a one-sided 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.

What is the difference between a one-sided limit and a two-sided limit?

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.

Why is it important to study one-sided limits?

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.

How can I teach myself about one-sided limits?

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.

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