Understanding Right-hand Limits: Exploring the Behavior of Functions as x Approaches a Given Point

right hand limit

A right-hand limit, also known as a one-sided limit, is a concept in calculus that allows us to determine the behavior of a function as it approaches a particular point from the right side

A right-hand limit, also known as a one-sided limit, is a concept in calculus that allows us to determine the behavior of a function as it approaches a particular point from the right side. It is denoted as follows:

lim(x → a+) f(x)

Here, “x → a+” indicates that x is approaching the value a from the right side.

To evaluate a right-hand limit, we follow these steps:

1. Determine the value at the point a: First, check if the function is defined at the point a. If it is, then the value of the function at that point is the right-hand limit.

2. Approach from the right: Secondly, find values of x that are slightly greater than a and evaluate the function at those points. As x gets closer and closer to a from the right side, observe the trend of the values. If the function approaches a specific value or diverges to infinity (positive or negative), that value is the right-hand limit.

It’s important to note that the function does not need to be defined at the point a for a right-hand limit to exist.

Here’s an example to illustrate the concept:

Given the function f(x) = 2x + 3, let’s evaluate the right-hand limit as x approaches 2:

1. Determine the value at the point a:
f(2) = 2(2) + 3 = 7

2. Approach from the right:
We can evaluate the function at x-values greater than 2:
f(2.1) = 2(2.1) + 3 = 7.2
f(2.01) = 2(2.01) + 3 = 7.02
f(2.001) = 2(2.001) + 3 = 7.002

As x approaches 2 from the right, we can see that f(x) approaches 7. Therefore, the right-hand limit as x approaches 2 is 7.

In summary, the right-hand limit allows us to understand the behavior of a function as x approaches a specific point from the right. By evaluating the function at x-values slightly greater than a, we can determine if the function approaches a particular value or diverges.

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