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 $f (x, y) = c_{1}$ and $f (x, y) = c_{2}$ intersect, then the curves are identical.

Short Answer

Expert verified

We proved that when $c_{1} = c_{2}$ , the planes are equal.

Step by step solution

Given information

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

Explanation

The equation of two variable can be given as

$a x + b y = c_{1}$ and $a x + b y = c_{2}$

Let the two plane intersect and intersection point be $(x_{0}, y_{0})$

Hence the equation of planes becomes

$a x_{0} + b y_{0} = c_{1}$ and $a x_{0} + b y_{0} = c_{2}$

As the right hand side is equal the left hand side also equals Hence we proved that when $w h e n c_{1} = c_{2}$

The planes are identical.

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Let $z = f (x, y)$ be a function of two variables. Prove that if the level curves defined by the equations $f (x, y) = c_{1}$ and $f (x, y) = c_{2}$ intersect, then the curves are identical.

Short Answer

Step by step solution

Given information

Explanation

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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

Step by step solution

Given information

Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Probability and Statistics

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Logic and Functions

Study anywhere. Anytime. Across all devices.

Let $z = f (x, y)$ be a function of two variables. Prove that if the level curves defined by the equations $f (x, y) = c_{1}$ and $f (x, y) = c_{2}$ intersect, then the curves are identical.