Question Video: Finding the Limit of a Function from Its Graph If the Limit Exists | Nagwa Question Video: Finding the Limit of a Function from Its Graph If the Limit Exists | Nagwa

# Question Video: Finding the Limit of a Function from Its Graph If the Limit Exists Mathematics • Second Year of Secondary School

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Using the graph shown, determine lim_(π₯ β 3) π(π₯).

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### Video Transcript

Using the graph shown, determine the limit as π₯ tends to three of π of π₯.

Here, we have the graph of π of π₯. And weβve been asked to find the limit as π₯ tends to three. We can see that at π₯ is equal to three, π of π₯ is defined to be negative five. However, when we are finding the limit of a function at a particular point, the value of that function at that point does not matter. What matters is whatβs happening to the function around that point. This is because the limit as π₯ approaches three of π of π₯ is defined to be the value π of π₯ approaches as π₯ tends to three. Letβs consider whatβs happening to π of π₯ to the left and to the right of π₯ is equal to three.

If we consider π of π₯ to the left of π₯ is equal to three, we can see that π of π₯ is increasing and getting closer and closer to the value of two, as π₯ is getting closer and closer to three. And as π₯ approaches three from the right, π of π₯ is again increasing. And it is also getting closer and closer to the value of two. Now, this tells us what we need to know about π of π₯ as π₯ tends to three, since from both the left and right, the value of π of π₯ approaches two as π₯ approaches three. And so, even though the value of π of three is equal to negative five, the limit as π₯ approaches three of π of π₯ is equal to negative two, which is our solution to this question. In this previous example, weβve seen how even though a function may be defined at a different point at a particular π₯-value, the limit as π₯ approaches that particular π₯-value of π of π₯ may be different to the value of π of π₯ at that point.

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