As .
Since the sine function oscillates, that means will oscillate between and quicker and quicker as .
Since will not tend to a single value, that means the limit does not exist and is thus discontinuous.
f(x) = sin(pi/x), when x != 0, and 0, when x = 0
Prove that f(x) is discontinuous in x = 0
Is it necessary to use the delta-epsilon-definition, or do you think i could sketch the graph and point to the jump in value?
If I need to use the definition, could someone give me a hint?