What is the linear taylor polynomial ?

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1 Answer
Jim G.
Mar 9, 2018

#f(x)=1/2x+pi/6-sqrt3/2#

Explanation:

#"using the following "color(blue)"odd/even identities"#

#•color(white)(x)sin(-x)=-sinx" and "cos(-x)=cosx#

#"Taylor series expansion is"#

#•color(white)(x)f(x)=sum_(n=0)^oo(f^n(a))/(n!)(x-a)^n#

#"here "a=-pi/3#

#f(a)=sin(-pi/3)=-sin(pi/3)=-sqrt3/2#

#f'(x)=cosx#

#rArrf'(a)=cos(-pi/3)=cos(pi/3)=1/2#

#rArrf(x)=f(a)+(f'(a))/(1!)(x-a)#

#color(white)(rArrf(x))=-sqrt3/2+1/2(x+pi/3)#

#color(white)(rArrf(x))=1/2x+pi/6-sqrt3/2larrcolor(blue)"linear"#

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