My Math Forum  

Go Back   My Math Forum > College Math Forum > Real Analysis

Real Analysis Real Analysis Math Forum


Thanks Tree1Thanks
  • 1 Post By SDK
Reply
 
LinkBack Thread Tools Display Modes
March 14th, 2018, 07:34 AM   #1
Senior Member
 
Joined: Dec 2015
From: Earth

Posts: 255
Thanks: 28

Equation from analysis

$\displaystyle lim_{y\rightarrow x} \frac{\sin y}{y}=1$
Find $\displaystyle x=?$
idontknow is offline  
 
March 14th, 2018, 08:54 AM   #2
SDK
Senior Member
 
Joined: Sep 2016
From: USA

Posts: 499
Thanks: 277

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
SDK is offline  
Reply

  My Math Forum > College Math Forum > Real Analysis

Tags
analysis, equation



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Analysis of Image superimposing using numerical analysis saugata bose Computer Science 0 March 8th, 2013 12:03 PM
Understanding some items on equation of fourier analysis nepdeep Real Analysis 3 March 7th, 2013 09:41 PM
Data analysis using Independent Component Analysis (ICA) ggyyree Advanced Statistics 1 August 9th, 2012 04:48 AM
Prove between Real Analysis and Complex Analysis uniquesailor Real Analysis 2 January 3rd, 2012 10:56 PM
Video discusses interesting new view of equation analysis Bon Qui Qui Number Theory 0 October 10th, 2011 01:11 AM





Copyright © 2018 My Math Forum. All rights reserved.