Use the MacLaurin series for f (x).

Compute the 10th derivative of

f (x) = arctan (x^2/4)

at x=0.

f^ (10) (0) =

Question

Mathematics

Dodson

14 July, 16:26

Use the MacLaurin series for f (x).

Compute the 10th derivative of

f (x) = arctan (x^2/4)

at x=0.

f^ (10) (0) =

+1

Answers (1)

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Brennan Smith · Answer 1

y = tan^-1 (x2/4) tan (y) = x2/4 sec2 (y) = x/2 y′ = xcos^2 (y) / 2 cos^2 (y) = 16x2+16 y′ = 8x / (x2+16)

let u be x2+16

du is 2x dx

dy = 4 du / u

y = 4 ln (x2 + 16)

y at x = 0 = 4 ln (16) = 11.09

Use the MacLaurin series for f (x).Compute the 10th derivative off (x) = arctan (x^2/4)at x=0.f^ (10) (0) =

Use the MacLaurin series for f (x).

Compute the 10th derivative of

f (x) = arctan (x^2/4)

at x=0.

f^ (10) (0) =