Question: Total. Points:

Size: px

Start display at page:

Download "Question: Total. Points:"

Adele Hutchinson
5 years ago
Views:

1 MATH 307 First Midterm October 6, 2010 Name: ID: Question: Total Points: Score: There are 5 problems on 6 pages in this eam (not counting the cover sheet). Make sure that ou have them all. You ma use a calculator if ou wish, provided our calculator does not do calculus. However, it is unlikel to be of much help. Do all of our work in this eam booklet, and cross out an work that the grader should ignore. You ma use the backs of pages, but indicate what is where if ou epect someone to look at it. Books, etra papers, and discussions with friends are not permitted. If ou wish to use our pschic abilities to read m mind for the answers, ou ma do so. However, remember that I ma be deliberatel thinking of the wrong answers during the test. You have about 79 minutes and 47 seconds to complete this eam. When ou complete this eam, if there is sufficient time it is strongl recommended that ou go back and reeamine our work, both on this eam and in our life up until now, for an errors that ou ma have made.

2 8 pts. 1. (a) Find the point of intersection of the lines 2 + t, 1 2t, 4 + t and 1 2s, 1 + s, 1 3s 8 pts. (b) Write the equation of the plane containing the two lines 2 + t, 1 2t, 4 + t and 1 2s, 1 + s, 1 3s You ma epress this either in vector/parametric form, or as an equation in,, and z. Note that this can be done even if ou couldn t do the first part. MATH 307: First Midterm Page 1 of 6 October 6, 2010

3 pts. 2. (a) Give all real values of a for which the matri 1 1 a has no inverse. 2 a pts. (b) Find the inverse of the matri If the matri has no inverse, sa wh not pts. (c) Find all solutions to the sstem of equations + = 2 + +z = z = 2. MATH 307: First Midterm Page 2 of 6 October 6, 2010

4 15 pts. 3. Department of Justice Special Agent Orange, while investigating charges of anti-competitive business practices, walks due east out of the MacroSoft corporate office building for a distance of eactl 26 meters. He pauses for a moment to tie his shoe, and suddenl he finds himself surrounded b an advancing wall of flames! He can t move, and there is no ground-based escape. However, he has his HookShot TM grappling hook with him, which he can fire at an fied object within 22.5 meters and pull himself to it. He recalls from his careful stud of the building plans that the nearest face of the building is a flat plane, inclined outwards with a normal vector of 4, 2 2, 1 relative to east (that is, in the coordinate sstem where east is 1, 0, 0 ). How far is Agent Orange from the nearest part of the building face? Can he escape, or is he 26m toast? MacroSoft MacroSoft MATH 307: First Midterm Page 3 of 6 October 6, 2010

5 8 pts. 4. (a) For the function F : R 2 R 3 given b F (, ) = cos(), sin(), 2, find the partials F (, ) and F (, ). 8 pts. (b) Write the equation of a plane tangent to the parametric surface s cos(st), s sin(t), 2t at the point ( 1, 0, 2π). MATH 307: First Midterm Page 4 of 6 October 6, 2010

6 12 pts. 5. Listed are si functions, labeled a through f. Underneath each surface below, write the letter of the function it is the graph of. a. ( + ) 2 b c. cos ( 2 + 2) d. 2 2 e. e ( ) ( ) 2 f. cos 2 z I IV z II V III VI MATH 307: First Midterm Page 5 of 6 October 6, 2010

7 This page was once a tree, and once it was blank. Now it is neither. You can make it less blank if ou like. Turning it back into a tree is more effort, but also more worthwhile.

Question: Total. Points:

Question: Total. Points: MATH 308 Second Midterm April 13, 2011 Name: ID: Question: 1 2 3 4 5 Total Points: 20 15 15 10 10 70 Score: There are 5 problems on 4 pages in this exam (not counting the cover sheet). Make sure that you