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highmath
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When have a function and I know by investigation of that it getting "bigger and bigger" or getting "smaller and smaller", how could I know that in infinity it continue by that way always?
So the function is "increasing" or "decreasing". But I have no idea what "in infinity" means. In Calculus, "infinity" is not a number- it makes no sense to talk about the value of a function, or any property of a function "in infinity" or "at infinity". We can talk about the limit of a function "as x goes to infinity".highmath said:When have a function and I know by investigation of that it getting "bigger and bigger" or getting "smaller and smaller", how could I know that in infinity it continue by that way always?
If I know that x goes to infinity, so how can I know how the function pattern is there?Country Boy said:function "as x goes to infinity".
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Calculus is a branch of mathematics that deals with the study of change and motion. It is used to analyze and model continuous change in various systems, such as in physics, engineering, economics, and other fields.
In calculus, infinity refers to the concept of a limit, where a function or sequence approaches a value that is infinitely large or infinitely small. It is used to describe the behavior of a function as its input approaches a certain value.
Infinity is used in functions to describe the behavior of the function at certain points or as the input approaches a certain value. It can also be used to determine the end behavior of a function, whether it approaches a finite value or goes to infinity.
Limits refer to the value that a function or sequence approaches as its input approaches a certain value, while infinity refers to the behavior of the function at that point or as the input approaches a certain value. Limits can approach either a finite value or infinity, while infinity is always a concept of an infinitely large or small value.
Calculus allows us to understand the behavior of functions as they approach infinity, whether it is in terms of growth, decay, or oscillation. It also helps us to determine the limits of functions and their end behavior, which can be crucial in solving real-world problems and making predictions.