FP2 (MEI) Maclaurin Series

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FP2 (MEI) Maclaurin Series

• Let Maths take you Further

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Finding and using Maclaurin series

• Before you startYou need to have covered the
  work on inverse trigonometrical functions.
• When you have finishedYou should
• Be able to find the Maclaurin series of a
  function, including the general term in simple
  cases.
• Appreciate that the series may converge only for
  a restricted set of values of x.
• Identify and be able to use the Maclaurin series
  of standard functions.

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The general binomial expansion
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Polynomial approximations
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Consider f(x) ex
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When x0
When x0
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For what values of x is this polynomial
approximation valid for?
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Autograph
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In general terms.
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Can you think of a standard function of x such
that the function and its derivatives evaluated
at zero are undefined?
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Can you explain why it is possible by referring
to the graphs of lnx and ln(1x)?
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All Maclaurin expansions are centred on x0. But
it is possible to form expansions centred
elsewhere. These latter two formulae are
alternative versions of the Taylor
approximations centred on xa. Notice Maclaurin
is a special case of a Taylor approximation
(using a0)
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Alternatively!!!!!
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There are three methods to consider well work
through the second method
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Finding and using Maclaurin series

• When you have finishedYou should
• Be able to find the Maclaurin series of a
  function, including the general term in simple
  cases.
• Appreciate that the series may converge only for
  a restricted set of values of x.
• Identify and be able to use the Maclaurin series
  of standard functions.

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Independent study

• Using the MEI online resources complete the study
  plan for Power series 1
• Do the online multiple choice test for this and
  submit your answers online.