Limits from a graph of a function

Sep 2007
6
0
Could someone explain why parts (a) and (b) are true? I initially thought that the limit does not exist (therefore false) but it turns out that the answer is true. I have been at this for a few days and I can't seem to figure out why.
 

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skeeter

MHF Helper
Jun 2008
16,216
6,764
North Texas
Could someone explain why parts (a) and (b) are true? I initially thought that the limit does not exist (therefore false) but it turns out that the answer is true. I have been at this for a few days and I can't seem to figure out why.
graph leaves much to be desired ...

what's happening with the graph between x = -1 and x = 1 ?
 

HallsofIvy

MHF Helper
Apr 2005
20,249
7,909
If the graph really is as shown, then f(x) is not defined between -1 and 0 and so, yes, neither \(\displaystyle \lim_{x\to -1^+} f(x)\) nor \(\displaystyle \lim_{x\to 0^-}f(x)\) are defined.

If the graph is the line y= 1 for x between -1 and 0, then the limits would be as given.