Question

Use the graph below to evaluate the limit as x approaches 2 of f of x:

Graph of a function that increases for x greater than or equal to 0 and less than 2 and is parabolic and increasing for x greater than 2 and less than or equal to 5. The point 2, 6 is marked on the graph

0
2
4
6

Answer 1

as you move from the left-side, and do just a left-sided limit, the left-sided limit is moving towards 4, now, it wil never get there, but for a limit, that's irrelevant, what matters is "what is it approaching?"

and now, doing a right-sided limit, it seems to be going to 4 as well,  now, it will never get there either, since f(4) = 6, but for a limit that doesn't matter.

so, since the left-sided and right-sided limits are going to 4, then the two-sided one is also going there too.