Understanding One-Sided Limits | Calculus Concepts Explained with Examples

One sided limit coming from the right

In calculus, a one-sided limit coming from the right refers to the behavior of a function as it approaches a specific point from the right-hand side

In calculus, a one-sided limit coming from the right refers to the behavior of a function as it approaches a specific point from the right-hand side. It is denoted by a superscript “+” or “→” on the variable in the limit expression.

Mathematically, if we have a function f(x), and we want to determine the one-sided limit of f(x) as x approaches a value c from the right, we write it as:

lim f(x) as x → c+

In this case, “x → c+” indicates that x is approaching c from the right side (values greater than c).

To calculate the one-sided limit, you would substitute values of x that are greater than c into the function f(x) and see if there is a consistent pattern in the resulting values. If the values of f(x) approach a specific number L as x gets closer and closer to c from the right side, then we say that the one-sided limit exists and is equal to L.

For example, let’s consider the function f(x) = 2x + 1. If we want to find the one-sided limit as x approaches 2 from the right side, we write:

lim (2x + 1) as x → 2+

To find this limit, we evaluate the function for x-values greater than 2, such as 2.1, 2.01, 2.001, and so on. If we find that the values of f(x) approach a specific number (in this case, it would be 5), then we can say that the one-sided limit as x approaches 2 from the right exists and is equal to 5.

Note that the one-sided limit can also be infinite, undefined, or not exist depending on the behavior of the function as x approaches the given value from the right.

It is important to distinguish one-sided limits from two-sided limits, where both the left and right behaviors of the function are considered as x approaches the given point.

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