Value that a function approaches, in math NYT

The crossword clue "Value that a function approaches, in math" with the answer "LIMIT" refers to a fundamental concept in calculus. In mathematics, a limit describes the value that a function or sequence approaches as the input approaches a certain point.

For example, as you get closer and closer to a particular value, the function's output gets closer to a specific number. This concept is crucial in understanding how functions behave at boundaries or asymptotic points. Thus, "limit" accurately fits the clue by representing the value that a function approaches in mathematical analysis.

The crossword clue "Value that a function approaches, in math" with the answer "ASYMPTOTE" refers to a line or curve that a mathematical function approaches but never actually reaches as it extends towards infinity. In calculus and algebra, an asymptote represents a boundary or limiting behavior of a function.

For example, in the function y=1xy = \frac{1}{x}y=x1​, the x-axis (y=0) serves as a horizontal asymptote because as x approaches infinity or negative infinity, the value of yyy gets closer to 0 but never actually becomes 0. Similarly, vertical and oblique asymptotes describe behaviors as the function approaches specific values along the x-axis or at certain angles. In summary, an asymptote is a conceptual tool used to understand the long-term behavior of functions and their graphical representations.

The crossword clue "Value that a function approaches, in math" with the answer "CONVERGENCE" refers to a fundamental concept in mathematics, particularly in calculus and analysis. Convergence describes the behavior of a sequence or function as it approaches a specific value, known as the limit, as the input (such as the number of terms or the independent variable) increases indefinitely.

In simple terms, if a function converges to a value, it means that as you continue to evaluate the function for larger and larger inputs, the outputs get closer and closer to a certain number, without ever deviating significantly from it. This concept is crucial in understanding the behavior of series, sequences, and functions within mathematical analysis, ensuring that despite the infinite nature of sequences, they can still have a finite and predictable outcome.

The crossword clue "Value that a function approaches, in math" with the answer "TENDENCY" refers to general direction or pattern that a function exhibits as it progresses towards a particular value or behavior. In mathematics, the term "tendency" isn't as precise as terms like "limit" or "convergence," but it implies that the function has a natural inclination or trend to move towards a certain value or outcome as the input increases or changes.

This could be understood as the function's general behavior over time or across a range of inputs, where it consistently leans or heads toward a specific value, even if it doesn't necessarily reach it exactly. The idea of a tendency in math highlights the broader pattern or direction in which a function evolves, which is essential in understanding long-term behavior or predictions.