Show that as a half range series of cosine terms for 0 < x < 1, /cos 2x cos 4x cos 6x + 12 2² 3² x(π-x) = π² 6 - +- + ..) ...
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- Find two power series solutions of (x2+2)y"+5xy'-y=0 about the ordinary point x=0. Include the first three terms of each series.Does the series of n=1 to infinity of (-1)^n*sin(9/n) converge or diverge?I have to find the first three non-zero terms of the Taylor series for (attached the equation below) about x = 1 (power series in (x − 1)).
- How many terms are needed in series of cos x to compute for |x| < (1/2) accurate to 1/2 decimal places(rounded)?Show that the Maclaurin series for 2e− x2√4 − x2is 1 −x2+x24+ · · ·.Hence,i. evaluate limx→02e− x2√4 − x2− 1x.ii. approximate the definite integral Z 0.40.12e− x2x√4 − x2dx correct to 4 decimalplaces.