taylor's & maclaurin's series simple
TRANSCRIPT
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Gujarat Power Engineeing And
Research InstituteSub :- Calculus
Topic :- Taylor’s and Maclaurin’s Series
Nikhil Patel (161040119038) Parth Patel (161040119040)Smit Patel (161040119043)Amit Prajapati (161040119047)
Created By :-Guided By :- Prof. Janki Gajjar
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Details
1) Taylor’s Series I. Definition II. Examples
2) Maclaurin’s Series I. Definition II. Examples
3) Standard Expand of Maclarin’s Series
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Taylor’s Series• Definition :- Let f be a function such that it
is infinitely many time differentiable in some open interval I at some internal point x=a. then the Taylor’s series generated by f at x=a is,
∑𝑛=0
∞ 𝑓 (𝑛 )(𝑎)𝑛 ! (𝑥−𝑎)𝑛= f (a )+ f ′ (a ) ( x −a )+f ′ ′ (a ) (𝑥−𝑎 )2
2 !+…
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• Let, x-a=h
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EXAMPLES(1) Expand in powers of x-3.
Ans. Hear x-a=x-3 So,a=3
We have to fine series about the point a=3.
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We put this value In Taylor’s series, We get
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(2) Using Taylor’s theorem find value of .
Ans.
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(3) Expand in power of .Hence find the value of . Ans: ) let
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Maclaurin’s Series• Definition :- Let f be a function such that it
has derivatives of all orders at x=0. then the Maclaurin’s series generated by f is,
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EXAMPLES(1) Find a Maclaurin’s series of .
We put this value in Maclaurin’s series we get,
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(2) Obtain a Maclaurin’s series for .
Ans. Here,
We put this value in Maclaurin’s series we get
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(3) Find Maclaurins’s series of .
Ans. Here,
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We put this value in Maclaurin’s series we get,
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Standard Expanssion of Maclaurin’s series
•
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Thank you...