(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

how do you show that sin(1/x) is continuous on (0,1)? (i know it's also continous on (0, infinite)).

2. Relevant equations

3. The attempt at a solution

|f(x)-f(xo)| = |sin(1/x)- sin(1/xo)|= |2sin((xo-x)\2)cos((xo+x)/2)|

=< 2|sin((xo-x)/(2xox))|=< |(xo-x)/(xox)|. is this inequality true? a similiar one is used in a different example. if it is, why? is it because sin(x)=<x ? when x is positive? now since x<1 choosing [tex]\delta[/tex]=xo[tex]\epsilon[/tex] then if

|xo-x|<[tex]\delta[/tex] then |f(xo)-f(x)|<[tex]\epsilon[/tex]

is this answer correct? what about the endpoints?

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# Homework Help: Continuity of sin(1/x) on (0,1)

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