1.

Use contour to do the following.

1. Plot the level curves of the function f ( x, y) = 3 y + y ³ ? x ³ in the region where x and y are between ?1 and 1 (to get an idea of what the curves look like near the origin), and in some larger regions (to get the big picture).

2. Plot the curve 3 y + y ³ ? x ³ = 5.

3. Plot the level curve of the function f ( x, y) = y ln x + x ln y that contains the point (1, 1).

2.

Find the derivatives of the following functions, and if possible, simplify each answer:

1. f ( x) = 6 x ³ ? 5 x ² + 2 x ?3

2. 

3. f ( x) = sin(3 x ² + 2)

4. f ( x ) = arcsin(2 x + 3)

5. 

6. f ( x) = x ^r

7. f ( x) = arctan( x ² + 1).

3.

See whether MATLAB can do the following integrals symbolically, and for the indefinite integrals, check the results by differentiating:

1. 

2. ? x sin( x ²) dx

3. 

4. 

5. .

4.

Compute the...