Limits Overview
Limit Notation (Left-Hand, Right-Hand, Overall)
Finding Limits Using a Graph
Finding a Limit Using Equations
Continuity

Right Hand Limit (RHL)

Right-Hand Limit (RHL) Notation:

lim x a + f ( x ) = y value

Read: The limit of f ( x ) as x approaches a from theright direction equals y .

The key to recognizing that you are looking at a right-hand limit will be the plus sign ( + ) in the exponent of your given a value .

Remember the a value that you are headed towards is an x value , and the answer to the limit question is always a y value .

A right-hand limit is asking you what y value does it look like your f ( x ) is heading towards as you approach the given a value from the right direction .

Starting from the right side (positive side) of the graph, follow along the graph (moving to the left), and head towards the a value you are given. Once you get to that a value the answer is the y value it looks like your graph is headed towards. You do not care if there is an actual value there (filled in circle) or if it is undefined there (open circle). The limit only cares what does it look like you are heading towards.

We are talking in terms of graphs for our f ( x ) here to better understand the concept. When you are asked to find these limits using an equation for f ( x ) , the process does not involve specifically following a graph visually. Instead, it is an algebra process. Meaning you will find your result using actual numbers and equations, and not simply look at the behavior of a given graph.

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