WEBVTT
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Determine the limit as π₯ tends to two of the function represented by the graph.
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Now, if we look at the graph, we can see that the function is called π of π₯.
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And weβve being asked to find the limit of π of π₯ as π₯ tends to two.
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In other words, this is the limit as π₯ tends to two of π of π₯.
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This can also be described as the value π of π₯ approaches as π₯ tends to two.
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So we need to find this value of π of π₯ using our graph.
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We can consider what π of π₯ is doing around the value of π₯ is equal to two.
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Weβll need to consider π of π₯ on both the left and right of two.
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Letβs consider π of π₯ on the right of π₯ is equal to two.
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We can see that as π₯ gets closer and closer to two, π of π₯ is decreasing.
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And it is decreasing towards this point here, which has a value of three.
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So we can say that as π₯ tends to two from the right, the value of π of π₯ approaches three.
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Letβs now consider what happens on the left of π₯ is equal to two.
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We can again see that as π₯ gets closer and closer to two, the value of π of π₯ is decreasing.
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And from the graph, we can see that it is decreasing towards the same value that π of π₯ is approaching from the right as π₯ approaches two.
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And thatβs a value of three.
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So now we can say that as π₯ approaches two from the left, π of π₯ approaches three.
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Since π of π₯ approaches the same value from the left and the right of two, we can therefore conclude that the value that π of π₯ approaches as π₯ tends to two is three.
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And so, we reach our solution, which is that the limit as π₯ approaches two of π of π₯ is equal to three.