Test1_Math3A03_solns.pdf - MATH 3A03 Test 1 Prof S Alama...

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MATH 3A03: Test 1 Prof. S. Alama Date: February 7, 2020 Duration: 50 min. Instructions: Fill in your name and student ID neatly in the box above. This exam consists of 4 problems, on 6 pages. The total number of points is 50. Indicate your answers clearly in the appropriate places. Justify your answers completely to obtain full credit. Cite any Theorems from class or the text that you may use. Scrap paper is also available for rough work. No books, notes, or calculators allowed. Good luck! YOU ARE RESPONSIBLE FOR ENSURING THAT YOUR COPY OF THE TEST IS COM- PLETE. LET THE INVIGILATOR KNOW OF ANY DISCREPANCIES.
Test # 1 / Math 3A3 -2- (1) [12 points] Let S = { q 2 Q | 0 q < p 2 } . (a) Fill in the values in the boxes: w = inf S = , u = sup S = (b) Complete the definition: Let S R be a nonempty bounded set. Then u = sup S if . . . (c) Use the definition of the supremum to verify your choice of u = sup S in part (a). SOLUTIONS 0 52 i n is an upper bound for S E X Eu V xes and 2 n is the smallest upper bound for S E H v n F xes with ve X E H e o I xes with U E x i Since

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