The limit as x approaches infinity of (x)(sin(1/x)) is definitively 1. This conclusion arises from recognizing that as x becomes unbounded, sin(1/x) approaches 0, creating the indeterminate form [0 * ∞]. The correct approach involves applying limit techniques to resolve this indeterminate form, rather than relying solely on algebraic manipulation. Graphical analysis further supports that the limit approaches 1.
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No.Michele Nunes said:Homework Statement
lim (x)(sin(1/x))
x->∞
Homework Equations
The Attempt at a Solution
The correct answer is 1, however I do not understand why. I thought that 1/∞ is essentially 0 and sin(0) = 0 so the whole limit would be 0.
Michele Nunes said:When I graphed it, the limit did seem to approach 1 though. I don't understand why it doesn't work out algebraically.
Ohh, I wasn't aware that 0 * ∞ is considered indeterminate form as well, but that's good to know now though, thank you!Mark44 said:No.
You have x becoming unbounded while sin(1/x) is approaching 0. This is the indeterminate form [0 * ∞], meaning that we can't say without taking the limits what will happen.