Find the absolute maximum and values of on the set -

Question

Question

1. Use any test to determine whether the series is absolutely convergent, conditionally convergent, or divergent.

∑_n=1^∞(-1)ⁿarctan(n)/n²

2. Find the absolute maximum and values of f on the set D.

f(x,y) = x²+ y² + x²y +4, D = {(x,y) ||x|≤ 1, |y|≤ 1}

3. Evaluate∫∫∫_Ey²dV , where is the solid hemisphere x²+y²+z² ≤9, y≥0.

4. Find the work done by the force field F(x, y, z) = (x, -y², y-z², z-x²) on a particle that moves along the line segment (0,0,1) to ( 2,1,0).

5. Use the Green's theorem to evaluate ∫_CF.dr.

F(x, y) = (√x2+1), tan-1(x), C is the triangle from (0, 0) to (1, 1) to (0, 1) to (0, 0).