WEBVTT
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this problem Number fifty with the sewer calculus Safe Edition
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section two point three Let f equal and this is
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a piece of ice function. So the first function
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is X squared, plus one if X is less
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than one and the quantity X minus two squared If
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X is greater than or equal to one party find
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the limit is exporters one from the left of F
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and the limit his expertise one from the right of
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f the limit as experts is one from the left
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of we'LL have to do with dysfunction. Since we're
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approaching one from the left, this only applies to
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this region. X is less than one, and
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so our function half will be X squared plus one
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and through directs an institution we played in one square
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two plus one gives us our value of two for
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the first limit for the second limit. The limit
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, his expressions that one from the right. We
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are in this region greater than or equal to one
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, which means that our function is Dequan titty X
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minus two squared and through direct institution one minutes Tuesday
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at one. It's quantity squared is positive. One
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. Prepare B does limit his expertise. One of
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enough exists. It does not exist because two does
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not equal one. The left limit is not equal
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to right. Lim. Therefore, this limit does
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not exist and finally for part. See, we
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need This gets aggressive. The function f we need
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to plot the first function for this region X is
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less than one and then plot. The second function
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, X minus two Quantity squared for X is greater
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than equal to one. Here's an example of ah
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plotting mechanism where the ranges that don't mean is restricted
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for each function. Hex QUOTABLES one is a parabola
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and as we can see as it purchased a positive
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one, that is where we a counter a hole
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. And then he jumped down to the next function
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explains to quantity squared where that continue function continues on
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after X is equal to one Here. We also
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see that the limit does not exist. That X
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equals two because the function approaches a different value two
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from the left than it does from the right one