Fall 2003 Prelim 2

# Fall 2003 Prelim 2 - MATH 192 FALL 2003 PRELIM 2 No...

• Notes
• 1

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MATH 192, FALL 2003 PRELIM 2 No calculators. An 8.5 x 11 in. sheet of paper with information on both sides is allowed. Please make sure to give adequate reasons for all your answers. 1. (10 points) Find equati0n(s) for the line L going through the points P(0, 1, 0) and Q(2, 3, 4). 2. (10 points) Consider the lines L1 : x = 2 + t, y = 2 + 3t, 2 2 4t and L2: \$=6+2s, y=4+s, zzO. a) Find the coordinates of the point of intersection of L1 and L2. b) Write an equation for the plane containing L1 and L2. 3. (10 points) a) Find the coordinates of the point of intersection of the line at = 2+ 3t, y = 1 +t, z = 4+ 2t and the plane 21: + 53/ + 2z = 2. b) Find the distance from the point (2, 1, 4) to the plane 22: + 5y + 22 = 2. 4. (10 points) Find the area of the triangle with vertices P, Q, and R, if P has coordinates (2, —3,0), Q has coordinates (5,1,2), the vector FR is parallel to i +j + k, and the vector (W is parallel to 4i + 8j. 5. (10 points) Find the volume of the box determined by the vectors u = 2i — j — k, v = j + 5k, and W = i + 3j. 6. (10 points) The velocity vector of a particle at time t is v(t) = egti 7 (sint —« 1)j — gt3k. a) Find the position vector of the particle r(t) if r(0) 2 i + j. b) Find the acceleration‘vector a(t). . . . . . . - . . x — y — 2 7. 10 pomts Find the hunt 1f 1t eXISts: 11m —————————. ( ) (z,y)n~(4,2) f — x/y + 2 8. (10 points) Find the limit if it exists: lim y sin(—1-). Chico—«010) :1: . . l 9. (10 pomts) Describe the domain and range of the function f :1:,y = ————— . Which < ) ~——y _ m, _ 2 of the following properties does the domain satisfy: open, closed, neither; bounded, unbounded? 6x ’ 8312 ’ agar 10. (10 points) Find the partial derivatives if f (51:, y) = \$6295” — cos(;ry). ...
View Full Document

• Fall '06
• PANTANO

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern