Question

How do I determine if a limit exist considering how it looks on a graph? Can I determine if a limit exists solely from the graph? Like can I determine if this limit exists solely from looking at the graph:

Answer 1

Answer: See below

Step-by-step explanation:

1. At x=1, the limit does not exist. If you see an open circle on the graph like you do here, you know that the function is discontinuous. This graph actually shows a jump discontinuity at x=1.

2.  You can determine if a limit exists by solely looking at the graph. Unfortunately in this case, f(1)=1 and $\lim_{x \to \ 1^-} f(x)$ are not equal to each other. Therefore, the limit does not exist.