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 March 14th, 2018, 06:34 AM #1 Senior Member   Joined: Dec 2015 From: somewhere Posts: 633 Thanks: 91 Equation from analysis $\displaystyle lim_{y\rightarrow x} \frac{\sin y}{y}=1$ Find $\displaystyle x=?$
 March 14th, 2018, 07:54 AM #2 Senior Member   Joined: Sep 2016 From: USA Posts: 642 Thanks: 406 Math Focus: Dynamical systems, analytic function theory, numerics $x = 0$ is the only solution. This follows since $\lim_{y \to x} \frac{\sin y}{y} = 1 \iff \lim_{y \to x} \sin y - y = 0$ But since $\sin y - y$ is a continuous function, we can compute this limit explicitly as $\lim_{y \to x} \sin y - y = \sin x - x$ and equating the 2 values for the limit implies $x$ satisfies $\sin x = x$ whose only solution is $x = 0$. Thanks from topsquark

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