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Chapter 12: Q. 70 (page 918)

Let z=f(x,y)be a function of two variables. Prove that when c1=c2the level curves defined by the equations f(x,y)=c1 andf(x,y)=c2 do not intersect.

Short Answer

Expert verified

By contradiction we proved that the planes do not intersect

Step by step solution

01

Given information.

We are given z= f(x,y)

02

Explanation.

The equation of the two variables can be given as

ax+by=c1and ax+by=c2

Suppose these two planes intersect ANd the intersection point be (x0,y0)

Hence the equation becomes

ax0+by0=c1and ax0+by0=c2

As the left-hand side of the equations is the same the right-hand side should be equal,

Hence we get, c1=c2

But we are given that c1鈮�c2

Hence our assumption is wrong the planes do not intersect

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