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Problem 26

In Exercises 21-28, use the graph to find the limit (if it exists). If the limit does not exist, explain why.$$\lim _{x \rightarrow 5} \frac{2}{x-5}$$

Answer

Limit does not exist

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## Discussion

## Video Transcript

I can't. And this problem We want to find the limit as X approaches five for this function f of X. So if you look at the graph of the facts, we see that there's a vertical pass and toke at X equals five. She kind of unsure of how you know that this expertise five him kind of look, the scaling of the graph. So if this right here is six, this one here, my must be four and two. So right in the middle should be X equals five. So So from the left. So we see that the left hand limit as we approach X equals five, appears to be going down towards negative infinity. So that left him in a minute. It is negative infinity, because it kind of keeps going down and down infinitely. And now if we look ATT behavior from the right, we see that the right hand who limit as we approach X equals five. It is going in a complete opposite direction. It's approaching positive, Anthony. So that is positive. Infinity. So since the left and right limits, I don't agree, and they are both infinite values. The limit does not exist, So he say limit does not exist. If the left right limits don't I agree? That's one case. Another case is when one or both of the limits are infinite value. So in this case, the women doesn't exist for both of those who since, actually so the limit is expert, just five for this function does not exist.