Q 51 - Calculus

Question

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

$f\left(x,y\right)=y csc x$

Step-by-Step Solution

Answer

The required level curves $c=-3,-2,-1,0,1,2,3$ for the function $f(x,y)=y csc x$ as shown as following :-

Step 1. Given Information

We have given the following function :-

$f(x,y)=y csc x$

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

Step 2. Graph of level curves

For each value of $c$, the level curve is the graph of the equation $f(x,y)=c$.

That is we have to graph the following equations :-

$$\begin{gathered} y csc x =-3 \\ y csc x =-2 \\ y csc x =-1 \\ y csc x =0 \\ y csc x =1 \\ y csc x =2 \\ y csc x =3 \end{gathered}$$

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