find the continuity of f(x) = {x, x0 It says it's continuous from (-infinity, 0) and (0,infinity) because the lim does not exist at x=0. WHy is that?

Question

find the continuity of f(x) = {x, x<= 0
                                              {x+1 >0
It says it's continuous from (-infinity, 0) and (0,infinity) because the lim does not exist at x=0. 

WHy is that?

anonymous · Answer

When you approach x = 0 from the left (negative x side), you use the top expression and the values of f(x) are x.

From the right, you use the lower expression.

You get different answers at x = 0, so at that point, it's not continuous, but everywhere else it is.

anonymous · Answer

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anonymous · Answer

so if i were to reach the same number it would have been continuous throughout?

anonymous · Answer

yes, but really you don't even need to "approach"  in this problem... you just need to look at the value of x at x=0 and realize that the function parts don't "connect"

anonymous · Answer

You'll get some problems eventually that require you to "approach" from either side because at the x=0 point, the function is undefined.  You don't really need that here... It isn't continuous at x=0 because it is not connected continuously, it's that easy

anonymous · Answer

okk that is clear to me