What is the term for the value that a function approaches as its input approaches a specified point?

What is the term for the value that a function approaches as its input approaches a specified point?

• A. Limit
• B. Bound
• C. Derivative
• D. Infimum

Answer: (A)

The limit is the value a function gets arbitrarily close to as its input gets arbitrarily close to a specified point. It describes how the function behaves near that point, even if the function isn’t defined there or equals a different value exactly at that input. For example, as x approaches 2, x^2 gets arbitrarily close to 4, so the limit is 4 even if the function’s value at x = 2 is something else or undefined. This distinguishes it from other ideas: a bound is just about staying within a range, not about converging to a specific value; a derivative is the slope or rate of change; and an infimum is the greatest lower bound of a set, not about approaching a point.

The limit is the value a function gets arbitrarily close to as its input gets arbitrarily close to a specified point. It describes how the function behaves near that point, even if the function isn’t defined there or equals a different value exactly at that input. For example, as x approaches 2, x^2 gets arbitrarily close to 4, so the limit is 4 even if the function’s value at x = 2 is something else or undefined. This distinguishes it from other ideas: a bound is just about staying within a range, not about converging to a specific value; a derivative is the slope or rate of change; and an infimum is the greatest lower bound of a set, not about approaching a point.