Final answer:
The question relates to the Intermediate Value Theorem, which states that for a continuous function on a closed interval [a, b], if l is a value between f(a) and f(b), then there exists a c in (a, b) with f(c) = l.
Step-by-step explanation:
The student's question pertains to a fundamental theorem in real analysis, specifically the Intermediate Value Theorem. This theorem states that if f is a continuous function on a closed interval [a, b], and l is any number between f(a) and f(b), then there exists a number c in the open interval (a, b) such that f(c) = l. This would apply to any function f that satisfies the premise: continuous on [a, b] and f(a) ≤ l ≤ f(b).
The information provided suggests different scenarios with factors such as n, l, me, and the constant product of a function f and a variable λ. However, these appear to be contexts for different mathematical principles and don't directly address the student's question regarding the Intermediate Value Theorem. The core concept here is the guarantee of the existence of a point c where the function reaches the value l within the interval (a, b).