Exam 5 Illustrations

1.  

             

2.

         

3.         

g(x, y) = 5x³ – 2xy²

           

4.

5.

        

Path g  goes from point (1, p) to (2, p/2) along a straight line.

6.

7.

Path g  goes from point ( 3, 1 )  to ( 5, 2 ) along a straight line.

8.

Path g  goes from point (p, –1) to (0, 1) along the curve  y = cos x.

9.

Path  g  goes along the boundary of the square,
from  (1,1) to (3,1) to (3,3) to (1,3) and back to (1,1).

11.   

g(x,y,z) =  x² cos y – sin(yz)

12.

13.

g  is the unit circle centered at the origin. 

14.

          z = 1 – x² – y²

Do you see the optical illusion?

15.

17.

  .........  Blue

Curl F  ........  Red