How to find the Maclaurin series of f(x)=cosx

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How to find the Maclaurin series  of f(x)=cosx

Nickolas Estes · Accepted Answer

Step 1. Define the Maclaurin seriesA function with an expansion series that provides the function&#039;s total derivatives is known as a Maclaurin series. The Maclaurin series of function f(x) up to order n may be found using Taylor series when x0=0General equation of Maclaurin series  isf(x)=f(x0)+f&#039;(x0)x-x0+f&#039;&#039;(x0)2!·x-x02+.....+fn(x0)n!·x-x0n=∑n=0∞fn(x0)n!·x-x0nAt x0=0f(x)=∑n=0∞fn(0)n!·xnStep 2. Find the derivative of the functionf(x)=cosx⇒f(0)=1f&#039;(x)=-sinx⇒f&#039;(0)=0f&#039;&#039;(x)=-cosx⇒f&#039;&#039;(0)=-1f&#039;&#039;&#039;(x)=sinx⇒f&#039;&#039;&#039;(0)=0fiv(x)=cosx⇒fiv(0)=1fv(x)=-sinx⇒fv(0)=0fvi(x)=-cosx⇒fvi(0)=-1Step 3. Find the Maclaurin series of the functionf(x)=f(0)+x·f(0)+x2f&#039;&#039;(0)2!+....+xnfn(0)n!Putting the above series we getf(x)=cosx=∑n=0∞(-1)n·x2n2n!=1-x22!+x44!-x66!+....Hence,  the Maclaurin series  of f(x)=cosx is 1-x22!+x44!-x66!+....

How to find the Maclaurin series of f(x)=cos(x)

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