Estimating Limit Values from Graphs AB & BC

To read $\lim_{x\to a} f(x)$ from a graph, trace the curve toward $x = a$ from the left and note the height being approached, do the same from the right, and compare. The two-sided limit is that common height when the sides agree and fails to exist when they do not. Nothing drawn at $x = a$ itself takes part: an open circle marks the height the curve approaches, a solid dot marks $f(a)$, and the two can differ or either can be absent.

Three errors recur. The most common is reading the solid dot instead of the trend, which answers the question of the function's value rather than its limit. The second is sampling one side only, or reading a coarse grid more precisely than it supports. The third appears at vertical asymptotes: writing that the limit equals infinity and treating that as an existing limit, when unbounded growth means the limit does not exist, and often the two sides run to opposite infinities.