   Chapter 14.1, Problem 55E

Chapter
Section
Textbook Problem

A thin metal plate, located in the xy-plane, has temperature T(x, y) at the point (x, y). Sketch some level curves (isothermals) if the temperature function is given by T ( x , y ) = 100 1 + x 2 + 2 y 2

To determine

To sketch: The level curves of the temperature function T(x,y)=1001+x2+2y2 .

Explanation

Given:

The temperature function is, T(x,y)=1001+x2+y2 .

Definition used:

“The level curves of a function f of two variables are the curves with equations f(x,y)=k , where k is a constant(in the range of f ).”

Calculation:

The equation of the level curves is k=1001+x2+2y2 .

Express the equation as follows.

k(1+x2+2y2)=100k+kx<

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