How to use a graph to determine a limit?

Question

anonymous · Answer

attachment

anonymous · Answer

I've nver understood how to use a graph to find the limit. I believe the limit does not exist, because they are approaching a different number from the right side of c from the left side of c. Am I right?

anonymous · Answer

@rational

anonymous · Answer

You're right about the overall limit approaching 2, but they're asking for the left and right side limits separately

anonymous · Answer

How do i find the left and right limits seperately? @peachpi

sparrow2 · Answer

just look when you aproach 2 on left side like 1,9 1,94, 1,98 and so on what function equals?  its' 5

amistre64 · Answer

find the point you fall off of

anonymous · Answer

As you follow the line from the left, it's at 5 , so the left limit is 5. The same to get the right is -3

amistre64 · Answer

if im walking along casually minding my own business from the left of 2 .. when i get to 2, at what point do i fall off?

anonymous · Answer

$$\lim_{x \rightarrow 2^-}f(x)=5$$
$$\lim_{x \rightarrow 2^+}f(x)=-3$$

anonymous · Answer

because those are the values you would be at if the graph didn't jump

anonymous · Answer

Oh my gosh thats it?? Thank you guys so much, I thought there was so much more to that.