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Calculus and Beyond Homework Help
Show that this piecewise function is continuous at 0
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[QUOTE="member 587159, post: 5988990"] You can't substitute that value if you want to use epsilon delta definition. You can however consider two cases: namely x = 0 and ##x \neq 0##. The former case gives always 0, so you can safely assume ##x \neq 0## and then you are allowed to plug in the expression. It then boils down to estimating ##|x \sin(1/x) - 0|## for ##x \neq 0##, given that x is small, which ought to be straightforward. [/QUOTE]
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Show that this piecewise function is continuous at 0
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