In the given equation as folows , use a computer algebra system to find the indicated Taylor polynomials for the function f. f(x)=\tan\pi x

snowlovelydayM

snowlovelydayM

Answered question

2021-09-13

In the given equation as folows , use a computer algebra system to find the indicated Taylor polynomials for the function f. Graph the function and the Taylor polynomials :-
f(x)=tanπx
(a)n=3,c=0

Answer & Explanation

Fatema Sutton

Fatema Sutton

Skilled2021-09-14Added 88 answers

Given,
f(x)=tanπx
n=3, c=0
Using, Taylor series of f(x) at c=0,n=3
f(x)=f(0)+f(0)(x0)+f(0)2!(x0)2+f(0)3!(x0)3
Now,
f(0)=tanπ(0)=0
The derivtaive of f(x) with respect to x,
f(x)=πsec2πx
f(0)=πsec2π(0)
f(0)=πsec20
f(0)=π(1)=π
f(x)=2πsec2πxtanπx
f(0)=2π2sec2π(0)tanπ(0)
f(0)=0
f(x)=ddx(2π2sec2πxtanπx)
f(x)=2π2ddx(sec2πxtanπx)
f(x)=2π2sec2πxddx(tanπx)+2π2tanπxddx(sec2πx)
f(x)=2π3sec4πx+4π3sec2πxtan2πx
f(x)=4π3sec4π(0)2π3sec2π(0)
f(0)=4π32π3

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