A student I tutor asked me this question. The L'Hopital's approach is quick and easy, but is there a direct but rigorous way to show this without invoking L'Hopital's?
2026-03-29 06:07:51.1774764471
Show that $\lim_{x \rightarrow 0} \frac{\sin(x)}{x} = 1$ without using L'Hopital's rule
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COMMENT.-In the circle of radius $1$ take the figure above and go to the limit.