Solve \( \nabla^{2} u=0, \quad 0 \leq x \leq a, 0 \leq y \leq b \) satisfying the \( B C s u(0, y)=0, u(x, 0)=0, u(a, b)=0 \) \( \frac{\partial u}{\partial x}(a, y)=T \sin ^{3} \frac{\pi y}{a} \)

Compute the work done by the force field \( F \) along the curve \( C \). \( \mathrm{F}(x, y)=\langle 2 x, 2 y\rangle, C \) is the line segment from \( (1,1) \) to \( (5,4) \) \( W=\square \)

Evaluate the line integral \( \int_{C} 5 x d s \), where \( C \) is the line segment from \( (1,2) \) to \( (8,7) \). \( \int_{C} 5 x d s=\square \)

3.- \( \quad f(x)=x \ln \cos x \)

Compute the divergence of \( F(x, y)=1.2 x i+1.75 y j \) \( \operatorname{div} F=\square \)

Compute the work done by the force field \( F=\langle y, 0, z\rangle \) along the triangle from \( (0,0,0) \) to \( (2,3,4) \) then to \( (2,3,0) \) and then back to \( (0,0,0) \). \( W=\square \)