Calculus-Sec-13-1-Solution

13.1    Multivariate Functions                          by SGLee - HSKim, YJLim, 구본우

1. If , find (a) , (b), (c) .

(a)

(b)

(c)

.

2. , find (a) , (b).

(a)

(b) .

3-4. Find the domain of the given function.

3.

$\small x^2-4y^2 \neq 0$  $\small \Rightarrow D=\left \{ (x,y) : x^2-4y^2 \neq 0 \right \}$

$\small D$ is domain of the function. (solved by 이지석 revised by 이원준)

4.

$\small y-4 \neq 0 , 16-x^2-z^2 \geq 0$ (solved by 이지석 revised by 이원준)

$\small \Rightarrow D = \left \{ (x,y,z) : y-4 \neq 0 , 16-x^2-z^2 \geq 0 \right \}$

$\small D$ is domain of the function.

5-6. Find the range of the given function.

5.

6.

7-9. Sketch a typical level surfaces of the function.

7.

8.

9.

10. Given that

,

find the  and intercepts of the level surface that passes through .