Compare and contrast continuity of a function?

[javier007]

PLEASE help me. I need to analyze the continuity of the piecewise function

f(x) = { sin(1/x) when x is not = to 0
_____{ 0_____ when x = 0

so i know sin(1/x) doent have a value at 0 but the second part of the function places the value of 0 at 0...BUT are both parts connected without any gaps, holes, or jumps in bewteen? in other words is it continuous or not?

I would appreciate it A LOT if you could explain it to me why or why not

thanks

 

[Office_Shredder]

Do you know how to tell if a function is continuous at a point?