Question 1

Answer 1(b): the volume under the surface f(x,y)=x2 above the square 0<=x<=1 and 0<=y<=1 in the xy plane.

Question 2Which vector field matches jxiy ˆˆ

Answer 2(4) You’ve got the whirlpool vector field!

Question 3Which vector field matches ixf ˆ)(

Answer 3(3) There is no j-hat component, and the length of the vectors depends only on the x-value.

Question 4

Answer 4(a) and (b) are both right…

Question 5Which vector field matches jyf ˆ)(

Answer 5(4) There is no i-hat component, and the length of the vectors depends only on the y-value.

Question 6Which vector field matches r

Answer 6(1) Don’t be silly, it couldn’t possibly be (2), since the vectors are all the same length!

Question 7

1) a-b-c 3)b-a-c

2) a-c-b 4)c-b-a

Answer 7(1). Since the integrand is always positive and the same in each integral, the only thing that matters is the size of the region we integrate over

Question 8Which vector field matches

r

r

Answer 8(2) Don’t be silly, it couldn’t be (1), all the vectors have different lengths

Question 9Which vector field matches jxf ˆ)(

Answer 9(1) There is no i-hat component, and the length of the vectors depends only on the x-value.

Question 10

Answer 10(b

Question 11Which vector field matches iyf ˆ)(

Answer 11(2) There is no j-hat component, and the length of the vectors depends only on the y-value.

Question 12The function that describes the distance a particle is from the x-axis as it follows a flow line is:(1) linear(2) exponential(3) sinusoidal(4) log

Answer 12(2) Since the vectors increase in length, the particle will be moving faster the further it is from the x-axis…

Question 13

Answer 13(a), (c), and (e) all give the area of the unit circle…

Question 14

Answer 14(c) gives the area of the unit circle…

Question 15

Answer 15(a) Is the only answer that doesn’t work

Question 16

Answer 16(b) The speed of the particle increases

Question 17

Answer 17(a) The radius of the circle increases

Question 18

Answer 18All answers except (d) parameterize this particle…