Question

"What is Limit as x approaches 2h(x), if it exists?"

Answer 1

I think it is 3 as a possible answer

Answer 2

The limit as x → 2 is 0. This is determined by the behavior of the blue-ish curve around x = 2.

When you're talking about a limit as x approaches some value c, you're really considering values of x ≠ c but very close to c. In this case, the blue-ish curve captures what happens around x = 2. To the left, the curve is falling toward 0, and to the right, the curve is falling further down from 0. The fact that f (2) = 3 (according to the green dot) has no effect on the value of the limit.