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Problem 66

Comparing Functions and Limits If the limit of $f(x)$ as $x$ approaches 2 is $4,$ can you conclude anything about $f(2) ?$ Explain your reasoning.

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## Video Transcript

in this problem were asked if the limit of Kovacs as X it'll just two is four and you conclude anything about half of to explain your reasoning. Now, well, we see this question you might think. Can we conclude that half of two is equal to four? Well, the answer to both questions is no. We will show that we cannot conclude anything about that, too. By providing a counter example to the claim that to limit has X perches, see is always equal to I have seen. So in this case, brass specifically about the women of every vex as X approaches to being four and the value of two. So let's look at the specific sample to the left. Here you see that the limit as X approaches to from the left appears to be four. And from the right, the limit also appears before so in our example, the limit as X approaches to this for however, if we look at the value of two, see that half of two is actually represented by filled in dot which has why value three. So we see that half of to is equal to three. Therefore, we cannot include anything about the value of coffee too. In general, the limit does not have to. I agree with Functioned. How you