Question

Use a graphing utility to graph six level curves of the function. $$ h(x, y)=3 \sin (|x|+|y|) $$

Short answer

The level curves are plotted in a graph where each curve represents the points (x, y) for which the function \( h(x, y) = c \). The plot would look a bit like a series of circular waves spreading out from the origin.

Step-by-step solution

Understanding What is Required

One needs to understand what is required. Here, the question requires the plotting of level curves. The function for which we need the level curves is \( h(x, y) = 3 \sin (|x|+|y|) \).

Determining the Level Curves

In general, level curves are obtained by setting the function equal to a constant. That is, the level curves for the function h are determined by \( h(x, y) = c \), where c is a constant. In the case of our given function, we need to solve \( 3 \sin (|x|+|y|) = c \), for x and y, where c is a constant value.

Plotting the Level Curves

Plot each of these curves on a graphing utility. This likely would involve a software or calculator capable of rendering multivariate functions. Ensure that the absolute values are accounted for in your plot.