The discussion revolves around evaluating the limit as x approaches infinity for the expression xsin(1/x). Participants explore the nature of this limit, which is characterized as an ∞.0 type limit due to the behavior of the sine function as its argument approaches zero.
The discussion is active, with participants providing hints and exploring different approaches to the limit. There is no explicit consensus on the best method, but several productive directions are being considered, including substitutions and references to established limits.
Participants are navigating the constraints of the limit's form and the behavior of the sine function as its argument approaches zero. There is an emphasis on understanding the implications of these mathematical relationships without reaching a definitive conclusion.
vanhees71 said:Hint
[tex]x \sin(1/x)=\frac{\sin(1/x)}{1/x}.[/tex]
Mark44 said:I wouldn't. This limit is related to this well-known limit
$$\lim_{t \to 0}\frac{sin(t)}{t}$$