Approximate f by a Taylor polynomial with degree n at

Redemitz4s

Redemitz4s

Answered question

2021-11-16

Approximate f by a Taylor polynomial with degree n at the number a.
f(x)=ln(1+2x), a=1, n=3,0.5x1.5

Answer & Explanation

Fesion

Fesion

Beginner2021-11-17Added 24 answers

Taylor polynomial with degree n at the number a is given by
f(x)Tn=r=0nfr(a)(xa)rr!
f(x)=ln(1+2x)f(1)=ln3
f(x)=2(1+2x)f(1)=23
f(x)=4(1+2)2f(1)=49
f(x)=16(1+2x)3f(1)=1627
Taylor polynomial with degree n=3 at the number a=1 is given by
f(x)T3=r=03fr(1)(x1)rr!
f(x)T3=f(1)+f(1)(x1)+f(1)(x1)22+f(1)(x1)36
f(x)T3=ln3+(23)(x1)+(49)(x1)22+(1627)(x1)36
f(x)T3=ln3+(23)(x1)(29)(x1)2+(881)(x1)3

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