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 Real Analysis Real Analysis Math Forum

 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 Tags analysis, equation Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post saugata bose Computer Science 0 March 8th, 2013 11:03 AM nepdeep Real Analysis 3 March 7th, 2013 08:41 PM ggyyree Advanced Statistics 1 August 9th, 2012 03:48 AM uniquesailor Real Analysis 2 January 3rd, 2012 09:56 PM Bon Qui Qui Number Theory 0 October 10th, 2011 12:11 AM

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