AP Calculus
Limits in Desmos
Desmos will not write ε-δ for you, but it is excellent at showing whether a limit exists and what value the graph is approaching.
Approach from both sides
Graph f(x), then add a slider a. Create a table of values just below and just above a. If the y-values agree, the two-sided limit likely exists. If they disagree, you have a jump.
Holes vs. vertical asymptotes
A hole looks like a missing point with matching left and right heights. A vertical asymptote sends y-values to ±∞. Zoom in; if the curve keeps climbing, it is not a removable discontinuity.
One-sided limits
Restrict the domain: f(x){x < 2} and f(x){x > 2}. Read the heights as x approaches the cut from each side. That is lim x→2⁻ and lim x→2⁺.