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Thank you We sneak and here's your shmoop du jour

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Brought to you by scottish mathematician colin mclaurin Few men

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have ever looked better in a dress Find the maclaurin

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series for e f of x equals x squared over

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one plus x And here the potential answers No What

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a mess All right first of all what the heck

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is the maclaurin series No not exactly Well in calculus

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the maclaurin series is the expansion of a function that

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revolves around x equals zero So this is the formula

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f zero plus f prime of zero x plus f

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double prime of zero over to factorial times x squared

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et cetera You get our drift here see the pattern

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We could make a tail and calculate the derivatives evaluated

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at zero to find the maclaurin series of function given

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But that would take some time And we're busy people

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We've got laundry to do a much more efficient ways

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to notice that x squared over one plus x equals

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x squared times one over one minus negative x Well

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we also know where we should know that The maclaurin

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series for one over one minus acts is the summation

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Of x to the power from any equal zero to

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infinity so substituting the negative acts into the summation notation

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and multiplying it by x squared we get x squared

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times The summation of negative x to the power from

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n equals zero to infinity still doesn't look like any

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of our answer choices so let's simplify it even more

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We can pull a negative one to the end out

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of the negative expedient and we can combine the x

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squared to the x to the end with the first

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basic exponents room Whenever you multiply to terms with the

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same base you can add the exponents Remember that Well

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we're left with negative one to the end and x

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to the power of end plus too so we're going

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with answer joyce b o sounds like our laundry's done 00:02:03.879 --> [endTime] well we'll get it tomorrow Oh

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