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4 Nov 2020: i) Calculate e. x2dx. [2]. (ii) Calculate the area enclosed by the curve r = a(1 cos θ), 0 6 θ < 2π, where a > 0. ... cos θ, sin θ,b/a)dr and r(sin θ, cos θ, 0)dθ. where r, θ and z are the usual cylindrical polar coordinates.

4 Nov 2020: with points . (2 cos v) cos u. (2 cos v) sin u. ... Your mission is to reach the point(x,y) = (B cos α,B sin α), where B > 0.

4 Nov 2020: r =λ. e cos θ 1 ,. where λ and e are non-negative constants. ... I(x) =. 3π. 0. e(tx cos t) dt. (b) Find the first two leading nonzero terms of the asymptotic expansion, as x , of theintegral.

4 Nov 2020: 1. 2I3. (ψ̇ φ̇ cos θ. )2 Mgl cos θ. ... V = V0(. cos(x) cos(2x)),. with positive constant V0. i) For very small V0, use the nearly-free electron model to compute explicitly the lowest-energy band gap to leading