State the domain and range of the function f(x, y, z) = 1/x ² + y ² + z ² .

Draw a quick, yet reasonably accurate graph of the following function. Label your axes in the usual (right handed) orientation.

F(x, y) = x ² + y ²

Find and skethc the level curves f(x, y) = c on the same set of coordinate axes for the given values of c. Label your curves.

Evaluate the limit.

By considering different paths of approach, show that the function has no limit as (x, y) ? (0, 0). Use accurate and appropriate notation.

Draw the branch (or tree diagram, and write the chain rule formula for ?p/?x and ?p/?y where p = k(r, s, t), r = h(x, y), s = f(x, y), and t = g(x, y).

Transcribed Image Text:

x - xy + 3 lim (x,y) →(1, -1) x ²y + 5xy - y ³ y4 - 2x² lim (x, y) (0,0) y 4 + x² x - xy + 3 lim (x,y) →(1, -1) x ²y + 5xy - y ³ y4 - 2x² lim (x, y) (0,0) y 4 + x²

Answer rating: 100% (QA)

1 Fx y z 1 x 2 y 2 z 2 Domain R 3 0 0 0 As the function becomes undefine... View the full answer