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Chapter 12: Q. 43. (page 917)

In Exercises 43鈥�52, sketch the level curvesc=-3,-2,-1,0,1,2,3

if they exist for the specified function

f(x,y)=x+y

Short Answer

Expert verified

They all represent straight lines.

Step by step solution

01

Given information

The given function isf(x,y)=x+y

02

The objective is to sketch the level curves for c=-3,-2,-1,0,1,2,3 

Consider the function f(x,y)in two variables, this function is in鈩�2

This function's graph will be in 鈩�3

Let the third variable is z

The equation of the graph is given as z=f(x,y)

The level curves of this function's graph are the graphs of the function for a constant value of z

Let z=cThe level curve of the graph at ' c'is defined as the graph of the equationf(x,y)=c

03

Use the above definition to determine the equation of the different required level curves.

x+y=-3x+y=-2x+y=-1x+y=0x+y=1x+y=2x+y=3

All of these are linear equations.

Therefore, they are all straight lines.

Plot these equations on same xy-plane

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