Test 3 Review

Test 3 Review

Test 3 Covers Sections - 11.7, 12.1-12.7, 13.1-13.2

To Study for Test 3:
1) Try these problems: Old Test 3 #3, 10, 11, Old Test 4 #1, 2, 4, 5, 8-9 Old Final Exam #5, 7
2) Know everything on this test review.
3) Study your homework problems and class notes from these sections.

For Section 11.7 you need to know:

1) To find local extrema:

a) Set

b) Find D =

(i) If D > 0 and
The local max. value = f(x, y).

(ii) If D > 0 and
The local min. value = f(x, y).

(iii) If D < 0,
The saddle point is (x, y, f(x, y))

(iv) If D = 0, then no conclusion.

2) To find absolute extrema on a closed bounded set D:

a) Set

b) Plug in all critical points into f(x, y) found in step (a) that lie in D. Also, determine the largest and smallest values on the boundary of D.

c) largest value from part (b) = absolute max.

smallest value from part (b) = absolute min.

Section 12.1-12.2 Double Integrals

1) Know how to set up and evaluate double integrals:

where D is a rectangular region or a general region bounded by 2 functions.

2) Memorize: V = SS ztop - zbottom dA
D

Section 12.3 Polar Regions

1) Memorize how to set up and evaluate double integrals over polar regions, R:

D R

2) Memorize:

Section 12.5 Triple Integrals

1) Know how to set up and evaluate triple integrals in rectangular, (x, y, z), coordinates:

2) Memorize that volume of E is given by:

( = SS ztop - zbottom dA )
D

Section 12.6 Triple Integrals in Cylindrical Coordinates

1) Memorize how to go from rectangular (x, y, z) to cylindrical (r,

2) Memorize how to evaluate triple integrals from rectangular into cylindrical coordinates:

E E

Section 12.7 Triple Integrals in Spherical Coordinates

1) Memorize how to go from rectangular (x, y, z) to spherical (

2) Know how to evaluate triple integrals from rectangular into cylindrical regions:

E E

Note: You will only be given dV =

Section 13.1 Vector Fields

1) Know how to sketch a vector field F(x, y) = <P(x, y), Q(x, y)> or be able to match it with its graph.

2) Know how to find and sketch = <

Sections 13.2 Line Integrals

1) Know how to evaluate line integrals in 2-D or 3-D:

where C:

Note: z, z(t), and

2) Memorize dx = x'(t)dt, dy = y'(t)dt, dz = z'(t) dt

3) Memorize how to evaluate the line integral of F (a continuous vector field) along C (i.e. Work done by F along C):