When do i need to check the sides to see if the limit exists? Do i do this only on multi type functions? Thanks!
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"Check the sides?" Can you give an example fo what you mean? Also, what is a "multi type function?" – saulspatz Aug 31 '19 at 15:07
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By checking the sides i mean finding the limit of x->x0 from left or right of x0.An example of a multi type function is this: f (x)=x if x>0 or f (x)=-x if x <-5 – user_ Aug 31 '19 at 15:09
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One of the definitions of the limit is that if $$L=\lim\limits_{x\to a^-} f(x) = \lim\limits_{x\to a^+} f(x)$$ then $$L=\lim\limits_{x\to a} f(x)$$
That is, the limit only exists if the left and right sided limits are the same. If, for example, you have reason to believe that a function (in your case, a piecewise function) is discontinuous at $x=a$, then you can try to find the left and right sided limits to see if the limit exists.
Andrew Chin
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This is only “half true” and can lead to misconceptions; see this question, for example: https://math.stackexchange.com/questions/637280/limit-of-sqrt-x-as-x-approaches-0 – Hans Lundmark Aug 31 '19 at 15:51