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and this problem were asked, is limit of f
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of X as X approaches si always equal to FFC
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fly Or why not? The answer to this claim
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is no. But we must show that we'll find
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a counter example to show that this is not sure
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. So if you look it here at the graph
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of the function, F of X will compute the
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limits and in computer off of C and C that
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the limit as X approaches Earth are seen is actually
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not going to be equal to FFC. So in
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this example, let's consider the graph of affects and
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let's see equal to Earth. No, if we
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look at the limits as X approaches three from the
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left and from the right, we'll see at the
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limit from the left is approaching this wide value here
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, which is three settlement from the left three as
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X approaches three no, and then the limit from
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the right. Coming from this direction is also three
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. So this tells us that the women exists and
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the limit is equal to three. However, if
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you look at the graph and we want to find
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effort three, you see that that's where the dot
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is filled in, which is at the Wye Valley
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. One so half of three is equal to one
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no, which is not equal to the limit.
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Thanks approaches. Three. So by this example,
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we've shown that the limit as X approaches scene for
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some function F of X is not always necessarily equal
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to the function value at that point.