CHM220H1 Study Guide - Quiz Guide: Parametric Equation, Partial Derivative
Document Summary
Problem 1 (5 marks) find parametric equations of the curve that is intersection of the ellip- soid x2 + y2 + 2z2 = 1 with the plane x + y = 1. 2 (2x 1)2 + (2z)2 = 1. Problem 2 (5 marks) sketch the level curves of the function f (x, y) = We want f (x, y) = c or with c 0 or 2x2 + (y + 1)2 = 1 are interested only positive values of c give possibly nonempty sets). If 1 c2 2 = 0 or c = 1 (recall that c 0) this is impossible. 2 so x = 0, y = 1. 2 level curves is given below in gure 1. = c or 2x2 + y2 + 2y + 3 = 1 c2 c2 2 with c 0 (since the square root is always positive we c2 2 < 0 or c > 1.
