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Compare the mathematical meaning of the word limit with its commonly used meanings. For the word’s mathematical meaning, think of how it was defined and used in this unit. For the word’s common meanings, start with the usage of limit as it is used in everyday speech, but also consider idioms and expressions that leverage the common meaning of limit in creative conversation.

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Answer:

Explanation:

The world "limit" means a value a function approches. The inputs get closer and closer to the numbers making it the basis of all calculus.

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The term "limit" is a complex concept with multifaceted meanings that vary depending on the context in which it is used. In the realm of mathematics, the notion of limit is a fundamental concept utilized for defining the continuity of functions, differentiation, and integration. A limit determines the behavior of a function as an independent variable approaches a particular value or infinity, and its mathematical definition is characterized by a precise set of rules governing its manipulation.

On the other hand, in everyday parlance, the word "limit" generally denotes a boundary or threshold beyond which something cannot surpass. It also denotes a cap on a quantity or a ceiling to which individuals can perform. Moreover, people often invoke the term "limit" to imply a restriction or constraint that hinders someone from acting in a certain way or realizing their full potential. For instance, one might say "there are limits to what I can endure" or "I'm at my limit."

Furthermore, "limit" is frequently employed in idiomatic expression such as "pushing the limits," "limitless possibilities," or "beyond the limits." These phrases suggest shattering boundaries and breaking through constraints to attain something extraordinary. The idea of "pushing the limits" encapsulates the notion of venturing into unchartered territories and disregarding all barriers along the way. In contrast, "limitless possibilities" refers to boundless opportunities and infinite potential that extend far beyond what we perceive as possible. Lastly, "beyond the limits" implies transcending conventional boundaries and venturing into unknown frontiers where anything is possible.

Overall, despite the overarching meaning of "limit" remaining consistent between mathematical and everyday usage, the applications of this term diverge significantly based on the context in which it is invoked. While in mathematics, the notion of limit is precisely defined, in everyday language, it is more commonly linked to restrictions or boundaries on individual potential. However, idiomatic expressions like "pushing the limits," "limitless possibilities," and "beyond the limits" convey a sense of adventure and the prospect of surpassing all obstacles to reach new horizons.

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