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Chapter 12: Q. 71 (page 918)

Let z=f(x,y)be a function of two variables. Prove that if the level curves defined by the equations f(x,y)=c1 andf(x,y)=c2 intersect, then the curves are identical.

Short Answer

Expert verified

We proved that whenc1=c2, the planes are equal.

Step by step solution

01

Given information

We are given a function of two variables z= f(x,y)

02

Explanation

The equation of two variable can be given as

ax+by=c1and ax+by=c2

Let the two plane intersect and intersection point be (x0,y0)

Hence the equation of planes becomes

ax0+by0=c1and ax0+by0=c2

As the right hand side is equal the left hand side also equals Hence we proved that when whenc1=c2

The planes are identical.

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