Question

Let f be the function given by the sum of the first three nonzero terms of this series. The maximum value of |lnx-f(x)| for .3<=x<=1.7 is:__________

Answer 1

Answer:

Step-by-step explanation:

f(x) = sin(4x)f'    = 4 cos(4x)f''   = -16 sin(4x)f'''  = -64 cos(4x)f⁽⁴⁾ = 256 sin(4x)f⁽⁵⁾ = 1024 cos(4x)The 4-th order Taylor series expansion isf(x+h) = f(x) + hf'(x) + (h²/2!)f''(x) + (h³/3!)f'''(x) + (h⁴/4!)f⁽⁴⁾(x) + ...The Maclaurin series is obtained by setting x = 0.Note that sin(0) = 0 and cos(0) = 1.The non zero terms aref(h) = 4h - (4h)³/3! + (4h)⁵/5! - (4h)⁷/7! + ...Answer: f(x) =4x- 4/3+4x/5+4x7

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