Question 1.Start on a new page. Total marks: 5+(3+3)+5+5 = 21.(a) Sketch the natural domain of the functionf(x, y) = ln (4-x2-y2).Use solid lines forportions of the boundary included in the domain and dashed lines for portions not included.(b) Supposez= cos(uv);u=exy;v=x2.Use the chain rule, after drawing an appropriate “treediagramme”, to find∂z∂xand∂z∂y.(c) Find parametric equations of a line through the origin and parallel to the linex= 1-t, y= 2, z= 3 + 4t.(d) Determine whether or not the following limit exists. If the limit exists, find its value.lim(x,y)→(0,0)1-cospx2+y2x2+y2.