Calculus
7th Edition
ISBN: 9781524916817
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 10.1, Problem 35PS
To determine
To find: the
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An interesting geometric model arises when one tries to determine the path of a pursuer chasing its prey. This path is called a curve of pursuit. These problems were analyzed using methods of calculus circa 1730 (more than two centuries after Leonardo da Vinci had considered them). The simplest problem is to find the curve along which a vessel moves in pursuing another vessel that flees along a straight line, assuming the speeds of the two vessels are constant.Let’s assume that vessel A, traveling at a speed a, is pursuing vessel B, which is traveling at a speed b. In addition, assume that vessel A begins (at time t = 0) at the origin and pursues vessel B, which begins at the point (1, 0) and travels up the line x = 1. After t hours, vessel A is located at the point P = 1x, y2, and vessel B is located at the point Q = 11, bt2 (see Figure 3.18). The goal is to describe the locus of points P; that is, to find y as a function of x.
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Problem 3.
Find the equation of the tangent plane to the graph of z = 4x³ + 3y² at the point above (x, y) = (1,2).
A. z = 4x + 3y - 20
B. z = 4x + 3y + 16
C. z = 12x+12y + 16
D. z = 12x+12y - 20
E. z = 16
Chapter 10 Solutions
Calculus
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