Question

Using the graph of f(x) below, find lim f(x), x ->3 -5 Does not exist 0 1.7

Answer 1

well, looking at the picture, coming from the right, namely lim -> 3⁺

starts off at 0 when x = 5, then as "x" moves to the left, it starts to go down and down and down, we have a dashed lilne at that section, namely is an asymptote, so there's a vertical asymptote at x = 3, which means that line keeps on going down to -∞.

now, coming from the left, namely lim -> 3⁻, starts off at 2 as "x" moves to the right it is going down and down and down towards the asymptotic line, so then coming from the left the limit is also -∞.

so one can say that $\bf \lim\limits_{x\to 3}~ f(x) = -\infty$, or it does not exist.