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Problem 11

Find the range of the functions. $$g(x, y)=\sqrt{16-4 x^{2}-y^{2}}$$

Problem 14

For the following exercises, find the level curves of each function at the indicated value of \(c\) to visualize the given function. $$z(x, y)=y^{2}-x^{2}, \quad c=1$$

Problem 15

For the following exercises, find the level curves of each function at the indicated value of \(c\) to visualize the given function. $$z(x, y)=y^{2}-x^{2}, \quad c=4$$

Problem 16

For the following exercises, find the level curves of each function at the indicated value of \(c\) to visualize the given function. $$g(x, y)=x^{2}+y^{2} ; c=4, c=9$$

Problem 17

For the following exercises, find the level curves of each function at the indicated value of \(c\) to visualize the given function. $$g(x, y)=4-x-y ; c=0,4$$

Problem 18

For the following exercises, find the level curves of each function at the indicated value of \(c\) to visualize the given function. $$f(x, y)=x y ; c=1 ; c=-1$$

Problem 19

For the following exercises, find the level curves of each function at the indicated value of \(c\) to visualize the given function. $$h(x, y)=2 x-y ; c=0,-2,2$$

Problem 20

For the following exercises, find the level curves of each function at the indicated value of \(c\) to visualize the given function. $$f(x, y)=x^{2}-y ; c=1,2$$

Problem 21

For the following exercises, find the level curves of each function at the indicated value of \(c\) to visualize the given function. $$g(x, y)=\frac{x}{x+y} ; c=-1,0,2$$

Problem 22

For the following exercises, find the level curves of each function at the indicated value of \(c\) to visualize the given function. $$g(x, y)=x^{3}-y ; c=-1,0,2$$

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