WEBVTT
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to evaluate this limit. We first do direct substitution
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. That means we replace each by zero and we
3
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get one over X plus zero squared minus one over
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X squared over zero. This gives us one over
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X squared minus one over X squared over zero or
6
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that's 0/0 An indeterminate value. This implies that we
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need to we write our function and so we have
8
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limit. As h approaches zero of we can combine
9
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the fractions in the numerator. That will be x
10
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squared minus X plus H squared over the common denominator
11
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, X plus H squared times X squared This times
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the reciprocal of age which is one over H.
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And then from here we can factor out the numerator
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and we get a limit As it approaches zero of
15
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we have x minus expose H times X plus expose
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each this all over X plus H squared times X
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squared Times one over age. And then from here
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we can simplify and we get the limit As it
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approaches zero of this one will be negative H.
20
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And then these times two x plus h over We
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have X plus H squared times X squared Times one
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over age. And then from here we can get
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rid of the age and we have limit As a
24
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church approaches zero of negative of two X plus H
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over we have X plus H squared times X squared
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. Now evaluating at zero. We get negative of
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two X plus zero over. We have explored zero
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squared times X squared which gives us negative two X
29
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over X squared times X squared dishes x rays to
30
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the fourth power. And you can simplify this further
31
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and we get negative two over X to the 3rd
32
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power. And so this is our limit.