Use this table of value to define the limit lim 𝑥→2 𝑓(𝑥) if possible. Explain your thinking.

Question

x=1.99	=1.999	x = 1.9999	x = 2	x = 2.0001	x = 2.001	x=2.01
y=1.9701	y=1.997001	y=1.99970001	y=2.5	y = 2.00030001	y=2.003001	y=2.0301

Answer 1

We want to know what f(x) is getting close to when x is getting close to 2. We can see that as x gets closer and closer to 2 from "the left" (when x < 2), y is getting closer and closer to 2 (it goes from 1.97 to 1.997 to 1.9997). We can see that as x gets closer to 2 from "the right" (when x > 2), y is getting closer and closer to 2 as well (it goes from 2.03 to 2.003 to 2.0003).

So, despite the fact that y is 2.5 when x is 2, y is approaching 2 when x approaches 2.