9.Let R be the annular region lying between the circles x2 + y2 = 1and x2 + y2 = 4. Evaluate the double integral dA.
8.Find the gradient ∇f(x,y,z) for the function given by f(x,y,z) = y2 + z2 - 4x, and also find the maximum value of the directional derivatives of f(x,y,z) at the point (1,2,-1).
7.Find the length of the arc from θ= 0 to θ= 2π for the cardioid r = f( θ) = 2 - 2cosθ.