Describe the level curves of function.

___________1. f (x,y) = 4x²+3y²

___________2. f(x,y,z) = 4x²+ 4y² - z²

Answer the following:

___________3. lim arctan(y/x)/(1+2xy)

___________5. If z = tan (2x-y), find f_x.

___________6. If f (x,y) = e^xsin(xy), find the second partial of f with respect to x and y.

___________7. If w = xycosz, x = t, y = t², and z = arccos t, find the first partial of w with respect to t.

___________8. Given: x+sec(y+2z) = 8, find the first partial of z with respect to y.

___________9. Find the directional derivative of the function, f (x,y) = e^-(x+y) at the point (0,0) in the

direction, v = i+j.

__________10. Find the gradient of the function, f(x,y,z)=ln (x+3y-4z) at the point, (4,1,0).

11. Show that the lim (xy)/(x²+y²) does not exist.

(xy)® (0,0) 

12. Given the graph of the function z = 4xy - x⁴ - y⁴. Find all relative maxima, minima, or points of

inflection.

13. Use Lagrange multipliers to find the indicated extrema for f(x,y) = 3x+y+10 under the constraint

x²y=6.

14. Set up the two equations that would be needed to solve the following problem.