University:
California State University, Northridge
Course:
MATH 250 | Calculus III
Academic year:

2015
Views:

336

Pages:

9
Author:

doodepsat9w0

MATH 250, Midterm 1 Name: (print) ______�_o_k __�_r_�o_K_,a,_J_____ This test includes 7 questions with the total of 50 points, on 9 pages. The last page is a formula reference. The duration of the test is 1 hour 15 minutes. Your scores: (do not enter answers here) 1 2 4 3 6 5 7 total 8 Important: The test is closed books/notes. A basic scientific calculator is allowed; no graphing calculators or other electronic devices. Give complete solutions to problems; no credit will be given for just the correct answers. 1. (6 points) (a) Find an equation for the sphere that passes through the point A(2, 0, -1) 1' and has center at 0(6, -3, -1). -,_ { 4C E'J"" I = . � I (6-2-)�-1--(-3-D) .,_-I- (-1- (-1)) .fC,.JI- 'P c:..e._ ..-e : c><-�) -t-y '2..- (v ,) {-3_/ -z- -1-- {P-r1)' ==- .:i.s 2 - (b) Does the sphere intersect the yz-plane? If yes, describe the curve of their intersection. .---z_ � (j,+3) + (-ar-1) = 5 (2-+r) - -II . > � ¥� ..:;/'oe,d '}Att)+ ��d � 7P -/1� • �� 3 ::,_ Page 2 a:; 2. (8 points) (a) Prove that for any two vectors a, bin �.3, ax b =-bx a. c� -e; - aJ -«;_/: f-- - � -6'2- t f 1 0 ( '"=a-. D - {a, -'J ?-� .t;)j -a;e �) /4, � �\ ? := ! ..., -? {--/ 4-L I ; (1 "-+ 1 ?.--t I "::::. .-?I fi.