Use the graph below to find the limits or explain why the limits do not exist.

Question

a) lim_x→2^- f(x)

b) lim_x→2^+ f(x)

c) lim_x→2 f(x)

It will not let me put the graph but it is a graph showing only the first quadrant labeled 1-5 on both axes.

One line has a slope of 1, passes through (0,3), and ends with an open dot at (2,5).

The other one has a slope of negative 1, passes through (5,1), and ends with an open dot at (2,4).

I hope that sufficiently described the graph. Thanks for any help.

Answer 1

lim x -> 2+ means the limit as you approach 2 from the positive (right) side

lim x -> 2- means the limit as you approach 2 from the negative (left) side

lim x-> 2 exists iff lim x-> 2+ exists, lim x-> 2- exists, and lim x-> 2+ = lim x-> 2-

Your open circles tell you your limits. I leave it to you to figure out which is which and whether the overall limit exists.