# Calculating Limits Approaching Infinity: An Example

• sapiental
In summary, limits approaching infinity refer to the behavior of a function as the independent variable increases without bound. The limit can be calculated by evaluating the function as x approaches infinity and can have a finite value. There is a difference between a limit approaching positive infinity and a limit approaching negative infinity, which describes the behavior of the function as x approaches infinity from the right and from the left, respectively. Real-world applications of calculating limits approaching infinity include studying the behavior of objects, analyzing market trends, and determining system capacity.
sapiental
I don't remember any rules on how to calculate limits approaching infinity.
for example, can someone please explain the following limit to me

(-1/2) lim (t->infinity) 1/(t^2 + 2) + 1/4 =

0 + 1/4 = 1/4

Thanks!

oh I think I get it now.. as t gets bigger the function -1/2 (1/(t^2+2)) approaches 0.. therefore we set it equal to 0?

Any feedback is much appreciated. Thanks!

Yes, that is the correct reasoning.

Thanks again.

## 1. What is the concept of limits approaching infinity?

Limits approaching infinity refer to the behavior of a function as the independent variable (usually denoted as x) increases without bound. In other words, it describes what happens to a function as x gets larger and larger.

## 2. How is the limit approaching infinity calculated?

The limit approaching infinity can be calculated by evaluating the function as x approaches infinity. This involves plugging in a very large value for x (such as 100 or 1000) and seeing what value the function approaches. If the function approaches a finite value, that is the limit. If the function approaches infinity or negative infinity, the limit does not exist.

## 3. What is the difference between a limit approaching positive infinity and a limit approaching negative infinity?

A limit approaching positive infinity describes the behavior of a function as x gets larger and larger, while a limit approaching negative infinity describes the behavior of a function as x gets smaller and smaller (towards negative infinity). This can also be thought of as the behavior of a function as x approaches infinity from the right and from the left, respectively.

## 4. Can a limit approaching infinity have a finite value?

Yes, a limit approaching infinity can have a finite value. This occurs when the function approaches a specific value as x gets larger and larger. For example, the limit of 1/x as x approaches infinity is 0, which is a finite value.

## 5. What are some real-world applications of calculating limits approaching infinity?

Calculating limits approaching infinity is used in various fields such as physics, engineering, and economics. For example, in physics, it is used to study the behavior of objects as they approach infinite speeds or distances. In economics, it is used to analyze the long-term trends and behaviors of markets. In engineering, it is used to determine the maximum capacity or efficiency of a system.

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