WEBVTT
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he is clear is that when you married hearing so
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we could use the limit comparison test with G of
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X equal to one over X square plus one.
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We're going to use the limit comparison tests as X
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approaches infinity for one over a square root of X
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to the fourth plus one over one over X Square
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plus one, which is equal to the limit as
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X approaches infinity for X square plus one over square
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root of X to the fourth plus one, which
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is equal to the limit as X approaches infinity for
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the square root of extra fourth plus two X Square
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plus one over X to the fourth plus one,
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which is equal to one. So since it's non
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mon zero for night number, it will either both
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converge or diverge. So we get from negative infinity
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to infinity. For D X over X square plus
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one, this is equal to the integral from negative
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infinity to zero for D X over X square plus
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one plus the interval From there oh, to infinity
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for D X over explore plus one. We know
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that G of X is even so. This can
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be re written as two come zero to infinity burn
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D over X over X square plus one which is
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able to to limit of a approaches Infinity there Oh
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, to a theatrics over at square pulse one,
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which is equal to two limit of the approaches infinity
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for inverse tangent from zero to a which is equal
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to two times pi house over minus zero is equal
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to pine. So this converges.