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8 January, 20:41

Use the MacLaurin series for f (x).

Compute the 10th derivative of

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

at x=0.

f^ (10) (0) =

+3
Answers (1)
  1. 8 January, 22:11
    0
    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
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