The third remainder for f (x) at x 0 is where c is a number between 0 and x Let f (x) cos x, as in Check Your Understanding Problem 11 1 (a) Find a number M such that f (4) (c) M for all values of c (b) In Check Your Understanding Problem 11 1, the error in using p 3 ( 12) as an approximation to f ( 12) cos 12 is given by R 3 ( 12) Show that this error does not exceed 8 64 10 6 R3 (x) (4) (c) 4 X

Question: The third remainder for f (x) at x = 0 is where c is a number between 0 and x. Let f (x) = cos

The third remainder for f (x) at x = 0 is R3 (x) = (4) (c) 4! X

where c is a number between 0 and x. Let f (x) = cos x, as in Check Your Understanding Problem 11.1.

(a) Find a number M such that | f ⁽⁴⁾(c)| ≤ M for all values of c.

(b) In Check Your Understanding Problem 11.1, the error in using p₃(.12) as an approximation to f (.12) = cos .12 is given by R₃(.12). Show that this error does not exceed 8.64 * 10^-6.

R3 (x) = (4) (c) 4! X

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