daniton Posted November 6, 2012 Share Posted November 6, 2012 (edited) Lim[sin(x)/x] as x ->0 Note-it is floor function Edited November 6, 2012 by daniton Link to comment Share on other sites More sharing options...
ajb Posted November 6, 2012 Share Posted November 6, 2012 What do you think the limit is? Why? Link to comment Share on other sites More sharing options...
daniton Posted November 8, 2012 Author Share Posted November 8, 2012 i have two things in my mind one the limit is 1 by using the property of limit in combination functions and since floor function is continuous at 1 that is the limit of sin(x)\x the other is when using squeezing theorem we say that x is slightly greater than sin(x) so the ratio is less than 1so the floor of this is 0. what do you say????????????? Link to comment Share on other sites More sharing options...
mathematic Posted November 9, 2012 Share Posted November 9, 2012 i have two things in my mind one the limit is 1 by using the property of limit in combination functions and since floor function is continuous at 1 that is the limit of sin(x)\x the other is when using squeezing theorem we say that x is slightly greater than sin(x) so the ratio is less than 1so the floor of this is 0. what do you say????????????? limit = 0 (your analysis is correct). Link to comment Share on other sites More sharing options...
daniton Posted November 9, 2012 Author Share Posted November 9, 2012 what about the first one?????? Link to comment Share on other sites More sharing options...
ajb Posted November 9, 2012 Share Posted November 9, 2012 I think it converges to 1 as x → 0. Link to comment Share on other sites More sharing options...
daniton Posted November 9, 2012 Author Share Posted November 9, 2012 why?? Link to comment Share on other sites More sharing options...
mathematic Posted November 9, 2012 Share Posted November 9, 2012 what about the first one?????? floor function is not continuous at integers. floor(1-x) = 0, floor(1+x) = 1, let x -> 0. Link to comment Share on other sites More sharing options...
alpha2cen Posted November 9, 2012 Share Posted November 9, 2012 (edited) why?? This is a graph. From the graph we can see sin(x)/x converses to 1 [sin (x)/x] is this graph. Edited November 10, 2012 by alpha2cen Link to comment Share on other sites More sharing options...
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