Question

Find a function f(x,y,z) whose level surface f=2 is the graph of the function g(x,y)= x+7y

Answer 1

Find a formula for a function g(x,y,z) whose level surfaces are planes parallel to the plane z = 2x+7y-3

Answer 2

Find a formula for a function g(x,y,z) whose level surfaces are planes parallel to the plane z = 2x+7y-3

Answer 3

What value of c makes the following function continuous at (0,0)?
f(x,y) = \begin{cases} x^{2}+y^{4}+4, & (x,y)\ne (0,0)\cr c, & (x,y) = (0,0)\cr \end{cases}

c =

Answer 4

Find the limit of the function
f(x,y) = \frac{\sin(5\sqrt{x^{2}+y^{2}})}{5\sqrt{x^{2}+y^{2}}}
as (x,y) \to (0,0). Assume that polynomials, exponentials, logarithmic, and trigonometric functions are continuous. [Hint: \lim_{t\to 0}\frac{\sin t}{t}=1.]