Question

find the third taylor polynomial for f(x) = 7/x expanded about c = 1

Answer 1

?

Answer 2

we need to calculate \( f^n(a) \)

Answer 3

a=1

Answer 4

it wouldn't be 7/x?

Answer 5

\( f(1)=7 \)

\( f'(1)=-7/1^2 =-7\)

\( f''(1)=(-7)(-2)/1^3 =7 *2\)

\( f'''(1)=(-7)(-2)(-3)/1^4 =-7 *2*3\)

\(f^{(4)}(1)= (-7)(-2)(-3)(-4)/1^5=7*2*3*4\)

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\(f^{(n)}(1)= (-7)(-2)(-3)(-4)...(-n)/1^{n+1}=(-1)^{n}*7*n!\)