Calculus
7th Edition
ISBN: 9781524916817
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Question
Chapter 11.1, Problem 28PS
To determine
To find: the traces of the given quadratic surface.
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Chapter 11 Solutions
Calculus
Ch. 11.1 - Prob. 1PSCh. 11.1 - Prob. 2PSCh. 11.1 - Prob. 3PSCh. 11.1 - Prob. 4PSCh. 11.1 - Prob. 5PSCh. 11.1 - Prob. 6PSCh. 11.1 - Prob. 7PSCh. 11.1 - Prob. 8PSCh. 11.1 - Prob. 9PSCh. 11.1 - Prob. 10PS
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- Sketch the surfaces ASSORTED 4y2 + z2 - 4x2 = 4arrow_forwardDetermine the shortest distance from the surface xy+3x+z2=12 to the origin.arrow_forwardWhat are the xy, yz, and xz traces if they exist and the type of surface (hyperboloid, etc) for the following:1. x2/25 + 9y2-4z2 -9 = 0 2. z = x2/25 - 9y2arrow_forward
- The paraboloid z=x^2 + y^2 intersects the plane x+y+z=1x+y+z=1 in the shape of an ellipse. The objective of this problem is to find the point on the ellipse closest and furtherest away from the origin. To this end, we establish the following constrained optimization problem: max/min f(x,y,z)=√x^2+y^2+z^2 s.t. z=x^2+y^2 x+y+z=1 To reduce the problem from three variables to two (i.e., removing z), substitute the first constraint into the objective function and square the result, then substitute the first constraint into the second constraint.arrow_forwardFind an equation of a generating curve given the equation of its surface of revolution. 8x2 + y2 + z2 = 5arrow_forwardA surface is defined by the following equation: 9x2 + 16y2 + 9z2 = 25. Make a sketch of the surface in the third dimension, marking the coordinates of the points where |x|, |y|, or |z| is maximized.arrow_forward
- Problem 1. What is the maximum vertical distance between the line y = x + 2 and the parabola y = x ^ 2, for −1 ≤ x ≤ 2?arrow_forwardPlease answer and show the complete solution for Item IV.Let S be the surface with equation given by 4x2- 9y2 = 9(z2 + 4).I. Find an equation of the trace of S on each of the coordinate planes and on the planes x = ±3√ 2. Determine if each trace is empty, a point, a (pair of) line(s), a parabola, an ellipse, or a hyperbola.II. What type of quadric surface is S?III. Using the traces obtained in I, provide a hand-drawn sketch of S. Label all important points (e.g. vertices) found on each trace.IV. View S as a surface of revolution. Find an equation of a generating curve on the xy-plane which, if revolved about the x-axis, will result to S.arrow_forwardWhat is the shortest distance from the surface xy +12x +z^2 =144 to the origin?arrow_forward
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