Function limits:
(Full development)

Answers:

The limit exists at -3

The limit does not exist at 0

The limit exists at 2, assuming your teacher allows positive infinity to be an answer (otherwise, the limit doesn't exist).

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Explanation:

If we start on the left side of x = -3, and approach toward x = -3 itself, then we will approach y = 1. Imagine it's like a car on a roller coaster able to move along the curve. If the car is to the left of x = -3, then it goes uphill slowly approaching that limiting value.

If we start on the right side of x = -3, and approach -3 itself, then we approach the same y value as before

So that's how I'm getting

The third limit is basically the combination of the first two limits. If the LHL (left hand limit) and the RHL (right hand limit) are equal, then the limit exists.

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We see that the LHL and RHL at x = 0 aren't the same. So the limit does not exist at x = 0

The LHL for x = 0 is 3 while the RHL for x = 0 is 0.

That explains why

DNE means does not exist

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Lastly, when we approach x = 2 from the left, we head upward toward positive infinity.

So

Also, because we're heading upward forever when approaching x = 2 from the right side.

We can then say

∈3,600

step-by-step explanation: