Use the graph of ...

Question

Use the graph of $h$ in the figure to find the following values or state that they do not exist.

${\displaystyle\lim_{x o4}h\left(x ight)}$

Accepted Answer

Welcome back everyone. In this problem, we want to refer to the graph of the function G to find the limit of G of X as X approaches five. Here we have our graph. And for answer choices, A says the limit is two B six C one and D says the limit does not exist. Now, how can the graph help us to find the limit of GF X as X approaches five? What do we know about the limit? Well, first of all, I recall, OK, that the limit, yeah, in this case, the limit or let me write it with a notation, the limit of G of X as X approaches five exist. OK. If the limit from the left hand side of G FX is equal to the limit from the right hand side of G of X or that value in this case five. So in other words, for us to find the limit, first, we need to establish if it exists, if both of those limits are the same and if they are, then their value is going to be the limit of G of X as X approaches five. So first, let's think about their limits. OK. Now, here this is the line at which X equals five. So now we're going to try and understand the behavior of G as X approaches five. Let's start from the left. What do you notice? Well, here notice that four function as X approaches five G approaches six. So that means our left hand limit. OK. The left hand limit of G FX is equal to six. What about our right hand limit? Well, now again, if we take it from the right, as X approaches five G of X also approaches six. OK. So we can say then that our right hand limit, the right hand limit of G FX is also equal to six. What do you notice? Well, now notice that the left hand limit E is equal to the right hand limit. So what this tells us then is that the limit exists. The limit as X approaches five of G of X exists and it is equal to six. If we go back to our answer choices that tells us, then that B is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

Use the graph of $h$ in the figure to find the following values or state that they do not exist. <IMAGE>
${\displaystyle\lim_{x\to4}h\left(x\right)}$

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Use the graph of $h$ in the figure to find the following values or state that they do not exist. <IMAGE>
${\displaystyle\lim_{x\to4}h\left(x\right)}$