Question

I need help identifying the limits in this graph.

Answer 1

Problem 1) Correct. Start at x = 2 and move slightly to the left of it. As you approach x = 2 along the curve, the y value fluctuates wildly not approaching a fixed value. This is why the lefthand limit (LHL) does not exist (DNE)

Problem 2) Correct. The right hand limit (RHL) does exist and the limiting value is 2. If you approach x = 2 from the right, you slowly get closer to y = 2

Problem 3) Incorrect. Because the LHL does not exist, this means that overall the limit at x = 2 DNE as well. You need to be able to approach it from both sides getting to the same value for the overall limit to exist.

Problem 4) Incorrect. If you approach x = 0 from either side, then you get to y = 0. So the limit does exist and the limiting value is 0. The answer for this box is 0.

Problem 5) Incorrect. The answer is DNE or undefined. The limit at x = 0 exists but the actual value does not. This is shown by the hole at x = 0.