10. Find the trigonometric polynomial F(x) of the form: for which the square error with respect to the given f(x) = x2 on the interval -π ＜x ＜ π is minimum. Compute the minimum value for N = 1,2, ....,5.(10分)

2. The tank in Fig. 1 contains 80 Ib of salt dissolved in 500 gal of water. The inflow per minute is 20 1b of salt dissolved in 20 gal of water. The outflow is 20 gal/min of the uniform mixture. Find the time when the salt content y(t) in the tank reaches 95% of its limiting value (as t→ ∞). (10 分)

10. Find the trigonometric polynomial F(x) of the form:
for which the square error with respect to the given f(x) = x² on the interval -π ＜x ＜ π is minimum. Compute the minimum value for N = 1,2, ....,5.(10分)

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