Ques 6 1.%3D%3DDiscuss the continuity of f(x,y). And show that f(x,y) and f,(x, y) exist at allpoints (x, y).4. Find the equation of parabola which has axis parallel to y-axis and which...

Ques 6

Extracted text: xy 3. Let f(x, y) =+y3n (X,y) # (0,0) (x, y) (0,0) where n> 1. %3D %3D Discuss the continuity of f(x,y). And show that f(x,y) and f,(x, y) exist at all points (x, y). 4. Find the equation of parabola which has axis parallel to y-axis and which passes through the points (0, 2), (-1,0) and (1, 6). An ellipse circumscribes a rectangle whose sides are given by x = ±2 and y = 4. If the distance between the foci is 4V6 and major axis is along y-axis, then find the equation of the ellipse. %3D 5. If w = In(x? + y2 + z?), x = ue" sin u, y = ue" cos u and z = ue", find %3D aw aw and using chain rule at the point (u, v) = (-2,0). dv п 6. Find the directions in which the function f(x, y,z) = In xy + In yz + In xz increase and decrease most rapidly at the point Po(1,1,1). Then find the derivatives of the function in those directions.