Question

State the x-values where the limit does not exist.

Answer 1

9514 1404 393

Answer:

• x = -2
• x = 2

Explanation:

There are vertical discontinuities in the function at x=-2, x=2, and x=4. When looking at limits, we find the function values to be different either side of those discontinuities at x = -2 and at x = 2. Thus, limits do not exist at those points (x = {-2, 2}).

At x=4, the discontinuity is in the function definition, not in the values left or right of that point. Hence the limit does exist at x=4, but the function is not continuous there.