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Chapter 12: Q 50 (page 917)

In Exercises 43-52, sketch the level curves c=-3,-2,-1,0,1,2,3if they exist for the specified function.

f(x,y)=cos(xy).

Short Answer

Expert verified

The required level curves c=-1,0,1for the functionfx,y=cos(xy)as shown as following :-

For c=-3,-2,2,3, the function does not exist, so there is no level curves for these points.

Step by step solution

01

Step 1. Given Information

We have given the following function :-

f(x,y)=cos(xy)

We have to graph the level curves c=-3,-2,-1,0,1,2,3for this function.

02

Step 2. Graph of level curves

For each value of c, the level curve is the graph of the equation fx,y=c.

We know that the cosine function lies between -1and1. So there will be no level curves for c=-3,-2,2,3

That is we have to graph the following equations :-

cos(xy)=-1cos(xy)=0cos(xy)=1

All of these level curves are hyperbolas.

Then we have the following graph of these level curves :-

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