S06_First_Midterm-D.Sarason

# S06_First_Midterm-D.Sarason - 8832832885 15:8 5188422415...

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Unformatted text preview: 8832832885 15:8? 5188422415 LICE MnﬂiIN LIERﬂiR‘r" F'nﬂiGE 81.385 Mathematics 16B February 15, 2006 Saracen. MIDTERM EXAMINATION 1 Name (Printed): Signature: SID Number: Tom Dorsey Zak Mesyan —gOTAL E David Penneys PSINPI‘E - Arun Sharma Section Number or Time: GSI (check one): DUDE] Put your name on every page. Closed book except for crib sheet. No calculators. SHOW YOUR WORK. Cross out anything you have written that you do not wish the grader to eoneider. Make Sure the grader can eeeily Spot your ﬁnal a.newer[s) to each question, for example by boxing the aneurers. The points for each problem are in parentheses. Perfect score 2 65. 8832832885 15:8? 5188422415 LICE MnﬂaIN LIERﬂR‘r" F'nﬂaGE 82.385 N ame 2 l. (15) For which values of a and f) (10133 the straight line 1: = mm + 17 give the best least-Squares approximation to the data points (0, O], (1, 2), (2, 3)? UHIZHIZUUIJ 1'3: U r” bllﬁb4224lb LILJH Mn'ﬂ'ulN LlHHIﬂuH‘r’ I-‘n'ﬂ'ullsilz Utlﬂﬁb Name 3 2. (20) For the function ﬁns, 3;) m 5:3 + 1/3 -~ 122: — 27y: (a) Determine the critical points. (b) Determine which critical points, if any, are saddle points. 8832832885 15:8? 5188422415 LICE MnﬂaIN LIERﬂR‘r" F'nﬂaGE 84.385 Name 41 3. (15) Evaluate the integral I = f/ (55-2 u y)d:cdy, where the region R is deﬁned by the R inequalities D 5 y :1 1, 172 :3 y. 8832832885 15:8? 5188422415 LICE MiﬂiIN LIERﬂiR‘r" F'iﬂiGE 85.385 Name ‘ 5 4. (15) AcCording to US. postal regulationa a rectangular package whose three side lengths measure 3: inches, 1; inches, 2: inches, must satisfy 2:1: + 23; + z E 84. Which values of 91,352 give the dimensions of a package whose diagonal has maximum length? (The length of the diagonal equals «£932 + y” + :52.) ...
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