3. Consider the 'pringle' surface S (see Figure 1) which is part of the graph z=ry inside the cylinder x² + y² = 2. Let C be the boundary of S, counterclockwisely oriented when viewed from above. (a) Set up, but do not evaluate, a definite integral that com- putes the line integral 2² ds. (b) Find the surface area of S. (c) Use Stokes' Theorem to evaluate (2³+ y) dr-2rydy + (1 + sin(2¹0)) dz. Figure 1. Pringle surface

Please answer all in detail. Thank you.

3. Consider the surface sin (xy)+ cos (xz)+ sin ( yz) =1. Find an equation for the tangent plane to the surface at the point (7,1,0).

Consider the curve y = – In|cos(x)| 77 as x travels from T to 6 a) Find the length of the curve. b) Find the surface area obtained from rotating the curve about the x-axis. c) Find the surface area obtained from rotating the curve about the y-axis.