mikkicastor05
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- Joined
- Sep 3, 2011
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Using the Larson 8th Calculus textbook (Ch1.4, pg. 76), it's discussing the intervals on which the piecewise function
g(x) = sin(1/x), x is not equal to 0
0, x=0
is continuous. It says the intervals of continuity are (-inf, 0) and (0, inf). I understand why sin(1/x) does not have continuity at 0.
My question is, why does the second part of the piecewise (g(x)=0, x=0) not make the entire function continuous on the entire real line?
g(x) = sin(1/x), x is not equal to 0
0, x=0
is continuous. It says the intervals of continuity are (-inf, 0) and (0, inf). I understand why sin(1/x) does not have continuity at 0.
My question is, why does the second part of the piecewise (g(x)=0, x=0) not make the entire function continuous on the entire real line?