Find the coefficient of x' in the expansion of: (а) (1 — г) -4г3 (c) x (1+ x* (b) (1 — г)-2т8 (d) (1+ x)'/² 5 ²)®(1– x)-3
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- For the given function defined on the interval(0, π), find1) expansion in Fourier series in real form by continuation of thefunction in odd and even way over total number axis;2) graphs for both ways of continuation.Solve until the 6th derivative and provide the summation notation of the taylor series. f(x) = ln 4x ; c= ¼let f be a function with second derivative f''(x)=sqrt 1+3x. the coefficient of x^3 in the taylor series for f about x=0 is
- For all 3 of the given 2`-periodical functionsdefined on the interval of the length 2`, find1) expansion in Fourier series in real form;2) the function of the sum of the Fourier series for each value of xthat belongs to the interval;3) graph of the sum of the Fourier series.Find the coefficient of x^3 in the taylor series about x=0 for f(x)=sin(2x)express f(x+h)=cos(x+h) in terms of x and h (step size) using the first 5 terms of taylor series. Show complete solution.