MATH 226 Study Guide - Midterm Guide: Medieval Commune, Iden, Multiple Integral
Document Summary
Be sure that this examination has 9 pages including this cover. Let s be the surface x2 + 4y2 9z2 = 1. a) Sketch the surface: find the equation of the tangent plane to the surface at (1, 3, 2). c) Suppose that a smooth curve c lies on the surface and passes through the point (1, 3, 2). Suppose also that the tangent line l to the curve c at (1, 3, 2) intersects the x-axis at some point q. The height of land in the vicinity of a hill is given, in terms of horizontal coordinates (x, y), by h(x, y) = A parking lot is to be built at (4, 5) and a hiking trail is to be made. The trail is to start at the parking lot and take the steepest route to the top of the hill: draw a contour map showing the height of land in the vicinity of the hill.
