The discussion focuses on finding the limit of the function f(x) as x approaches 0, specifically lim x→0 x^4f(x), under the condition that 0 ≤ f(x) ≤ 1. Participants clarify that the limit evaluates to 0 when f(x) approaches 0 and to 1 when f(x) approaches 1. The "squeeze theorem" is identified as a crucial concept for proving the limit exists and is equal to 0, as it effectively bounds the function between two limits. The conversation emphasizes the importance of understanding the behavior of f(x) within the specified constraints.
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Don't you mean 0 ≤ f(x) ≤ 1?thatguythere said:Homework Statement
Suppose 0 ≤ f(x) ≥ 1 for all x, find lim x→0 x^4f(x)
thatguythere said:Homework Equations
The Attempt at a Solution
I'm very uncertain about how to go about doing this.
lim x→0 x^4 f(x) = 0^4 (0)
= 0
lim x→0 x^4 f(x) = 1^4 (1)
=1
How does that prove anything?