CALCULUS EARLY TRANS.LLF W/WEBASSGN CODE

9th Edition

ISBN: 9780357537305

Author: Stewart

Publisher: CENGAGE L

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Chapter 14, Problem 2PP

Marine biologists have determined that when a shark detects the presence of blood in the water, it will swim in the direction in which the concentration of the Wood increases most rapidly. Based on certain tests, the concentration of blood (in parts per million) at a point P(x, y) on the surface of seawater is approximated by

C(x, y) = e^{−(x2 + 2y2)/10x}

where x and y are measured in meters in a rectangular coordinate system with the blood source at the origin.

(a) Identify the level curves of the concentration function and sketch several members of this family together with a path that a shark will follow to the source.

(b) Suppose a shark is at the point (x₀, y₀) when it first detects the presence of blood in the water. Find an equation of the shark's path by setting up and solving a differential equation.

System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.

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Chapter 14, Problem 1PP

Chapter 14, Problem 3PP

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Chapter 14 Solutions

CALCULUS EARLY TRANS.LLF W/WEBASSGN CODE

Ch. 14.1 - If f(x,y)=x2y/2xy2 , find (a) f(1,3) (b) f(2,1)...Ch. 14.1 - If g(x,y)=xsiny+ysinx , find (a) g(,0) (b)...Ch. 14.1 - Let F(x,y,z)=yx2z . (a) Evaluate F(3,4,1) . (b)...Ch. 14.1 - Let f(x,y,z)=lnzx2+y2 . (a) Evaluate f(4,3,6) ....Ch. 14.1 - Find and sketch the domain of the function. 7....Ch. 14.1 - Find and sketch the domain of the function. 8....Ch. 14.1 - Find and sketch the domain of the function. 9....Ch. 14.1 - Find and sketch the domain of the function. 10....Ch. 14.1 - Find and sketch the domain of the function. 11....Ch. 14.1 - Find and sketch the domain of the function. 12....

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Solution Summary: The author explains the level curves of a concentration function C(x,y)=e

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Chapter 14 Solutions