BSc Mathematics SEM I 2016 17 2016-17 ATKT MATHS I Question Paper - Mumbai University | munotes

Questions asked in this paper

1. Q2 Define absolute value and State of absolute value,
2. Q3 State and prove Hausdorff Property of neighbourhood in IR and prove AM ~GM inequality of
3. Q2 Attempt any one, [each 8] 1). State all algebric properties of sequences
4. Q2 | Define the Cauchy sequence in IR and show that following sequences are not Cauchy in [R
   • (b) Attempt any three. [each 4]
5. Q1 and prove Sandwich theorem for
6. Q2 Show that every mcnotonic increasing sequence is bounded below,
7. Q3 Prove that if a, &b, are two sequenc g and b respectively then prove + bn) and (An + by) +
8. Q3 ; (a) Attempt any one. [each 8] Let f, g be real valued function defined on subset S'/R and = g(x) = mthen prove that
   • (b) Attempt any three. [each 4] | J ) Define the following functions and draw the graphs
9. Q2 Define right hand and hand limits and evaluate right and left hand limits fas f(x) in following case
10. Q3 Let J > IR be continuous at P J where an open interval in IR prove that f + J IRis continuous at P 4 4) Prove that Let f be real valued function on subset of IR. Let P 4 f(x)exists then itis unique Attempt any three. [each
11. Q1 Detine 6 definiton of of a function at a point P also graphical meaning of continuity of a function
12. Q2 Discuss the boundedness of 5 : (x/3 <x <7}, S= {sin x/x Prove that limp =0 Prove that x then such that 0 <
13. Q5 Exaniine whether the followin: sequences are monotonic 7 i) an, = —~ii) an = = 4 6) Prove that if a,&b,are convergent sequences having limits a and b ! respectively then prove that (a, + 1,,) converges and + by) = at b

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