8. The Taylor series about x = 3 for a certain function f converges to f(x) for all x in the interval of convergence. The nth derivative off at x = 3 is given by (-1)" n! 5" (n+3) f(n) (3) = and f(3) = 3 1 (c) Show that the third-degree Taylor polynomial approximates f(4) with an error less than 4000

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8. The Taylor series about x = 3 for a certain function f converges to f(x) for all x in the interval of
convergence. The nth derivative off at x = 3 is given by
(-1)" n!
and ƒ (3) = -3
5" (n+3)
f(n) (3)=
1
(c) Show that the third-degree Taylor polynomial approximates f (4) with an error less than 4000
Transcribed Image Text:8. The Taylor series about x = 3 for a certain function f converges to f(x) for all x in the interval of convergence. The nth derivative off at x = 3 is given by (-1)" n! and ƒ (3) = -3 5" (n+3) f(n) (3)= 1 (c) Show that the third-degree Taylor polynomial approximates f (4) with an error less than 4000
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