Find the Taylor polynomials of orders 0, 1, 2, and 3 generated by ƒ at...

glasskerfu

glasskerfu

Answered

2021-09-03

Find the Taylor polynomials of orders 0, 1, 2, and 3 generated by ƒ at a.
f(x)=x,a=4

Answer & Explanation

2k1enyvp

2k1enyvp

Expert

2021-09-04Added 94 answers

Consider the provided function,
f(x)=x,a=4
Find the Taylor polynomials of orders 0, 1, 2, and 3 generated by ƒ at a.
The Taylor polynomial is shown below,
Pn(x)=f(a)+f(a)2!(xa)2++fk(a)k!(xa)k+
First find the derivative of the function,
f(x)=x
f(x)=12x
f(x)=14x32
f(x)=38x52
Substitute a=4 in the above functions we get,
f(4)=42
f(4)=12414
f(4)=14(4)32132
f(4)=38(4)523256
So, the Taylor polynomials of orders 0, 1, 2, and 3 is shown below.P0=2
P1=2+14(x4)
P2=2+14(x4)+164(x4)2
P3=2+14(x4)+164(x4)2+31536(x4)3
Hence.

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