Bachelor of Science (B.Sc.) Sem I 2015 2016 Maths L Question Paper - Mumbai University | munotes

Questions asked in this paper

1. Q1 Find LUB and GLB of S = { /n IN}
2. Q2 State and prove inequality of IR
3. Q3 State and prove Hausdorff property of neighbourhood
4. Q4 Prove that if a, is convergent sequence then it is bounded
   • (a) Attempt any one. [each 8]
5. Q1 State and prove Sandwhich theorem for sequence
6. Q2 State all algebraic properties of sequences,
   • (b) Attempt any three. [each 4]
7. Q1 Prove that i) if a, > aa
8. Q2 Prove that if a, #0 for then
9. Q3 Show that a, > |a,| > jal
10. Q4 Define monotonic increasing and decreasing sequence and give example then prove that f > IR is continuous at P
11. Q4 Attempt any three
12. Q2 Let fbe eal valued defined on subset /R. Let P 1, if a WO convergent si quences naving limits a and b

Read from the scan above, so a character or two may differ. The scan is the original.