A parabola has a focus of F (8.5,-4) and a directrix of x=9.5.
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The taylor series for the f(x)=8/x centered at the given value of a=-4 is -2+2(x+4)/1!-24/16 /2!+...........
Given a function f(x)=9/x,a=-4.
We are required to find the taylor series for the function f(x)=8/x centered at the given value of a and a=-4.
The taylor series of a function f(x)=
Where the terms in f prime (a) represent the derivatives of x valued at a.
For the given function.f(x)=8/x and a=-4.
So,f(a)=f(-4)=8/(-4)=-2.
(a)=
(-4)=-8/(
=-8/16
=-1/2
The series of f(x) is as under:
f(x)=f(-4)+
=-2+2(x+4)/1!-24/16 /2!+...........
Hence the taylor series for the f(x)=8/x centered at the given value of a=-4 is -2+2(x+4)/1!-24/16 /2!+...........
Learn more about taylor series at brainly.com/question/23334489
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