The function g(x) = { 1 for -1 for 1< x<0 0 . am Pm (x) m=0 where for m + n, 1 | Pm(x)P(x) dx = 2 for m = n. 2m + 1 Find the first two non-zero am of the series.

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Q: Find a power series for the function f (x) = x2/(1 + x3)

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Q: 3. Find the Fourier series for the following function: f (x) = 64x³ for the interval (-n, 1) %3D

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Q: -2 (x) 1/2 [ 2 X

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.