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Magazine Problem 23
For the following exercises, find the level curves of each function at the indicated value of \(c\) to visualize the given function. $$g(x, y)=e^{x y} ; c=\frac{1}{2}, 3$$
Problem 24
For the following exercises, find the level curves of each function at the indicated value of \(c\) to visualize the given function. $$f(x, y)=x^{2} ; c=4,9$$
Problem 25
For the following exercises, find the level curves of each function at the indicated value of \(c\) to visualize the given function. $$f(x, y)=x y-x ; c=-2,0,2$$
Problem 26
For the following exercises, find the level curves of each function at the indicated value of \(c\) to visualize the given function. $$h(x, y)=\ln \left(x^{2}+y^{2}\right) ; c=-1,0,1$$
Problem 27
For the following exercises, find the level curves of each function at the indicated value of \(c\) to visualize the given function. $$g(x, y)=\ln \left(\frac{y}{x^{2}}\right) ; c=-2,0,2$$
Problem 28
For the following exercises, find the level curves of each function at the indicated value of \(c\) to visualize the given function. $$z=f(x, y)=\sqrt{x^{2}+y^{2}}, \quad c=3$$
Problem 30
For the following exercises, find the vertical traces of the functions at the indicated values of \(x\) and \(y\), and plot the traces. $$z=4-x-y ; x=2$$
Problem 31
For the following exercises, find the vertical traces of the functions at the indicated values of \(x\) and \(y\), and plot the traces. $$f(x, y)=3 x+y^{3}, x=1$$
Problem 32
For the following exercises, find the vertical traces of the functions at the indicated values of \(x\) and \(y\), and plot the traces. $$z=\cos \sqrt{x^{2}+y^{2}} \quad x=1$$
Problem 33
Find the domain of the following functions. $$z=\sqrt{100-4 x^{2}-25 y^{2}}$$
