Suppose f(2) = 1, f'(2) = 1, f"(2) = 0,

tearstreakdl 2021-12-18 Answered
Suppose f(2) = 1, f'(2) = 1, f"(2) = 0, and f(3)(2) = 12.
Find the third-order Taylor polynomial for f centered at 2 and use this polynomial to estimate f(1.9).
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Expert Answer

Debbie Moore
Answered 2021-12-19 Author has 43 answers
Step 1:Concept
Taylor polynomial is
f(x)=f(a)+f(a)(xa)+f(a)(xa)22!+f(a)(xa)33!+
Step 2:Solution
Plugging the values at a=2
f(x)=f(2)+f(2)(x2)+f(2)(x2)22!+f(2)(x2)33!
=1+1(x2)+0(x2)22+12(x2)33!
=1+x2+2(x2)3 At x=1.9
=1+1.92+2(1.92)3f(1.9)=0.898
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eskalopit
Answered 2021-12-20 Author has 31 answers
Given,
f(2)=1,f(2)=1,f(2)=0,f3(2)=12
f(n)=f(a)+f(a)(na)+f(a)(na)22!+f(a)(na)33!
f(n)=f(2)+f(2)(n2)+f(2)(n2)22!+f(2)(na)33!
=1+1(n2)+(0)(n2)22+12(n2)36
=1+n2+0+2(n2)3
f(n)=2(n2)3+n1
f(1.9)=2(1.92)3+1.91
=2(0.1)3+09=2(0.001)+0.9
=0.9-0.002
=0.878
f(1.9)=0.878
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