Analysis 1 (MATS2101)
Mathematics and Computer Science - MCS
Semester: First Semester
Level: 200
Year: 2018
University of Bamenda
Faculty of Science
Department of Mathematics and Computer Science
Continuous Assessment
Course Title: Analysis 1.
Course Code: MATS2101.
Duration: 2 hrs.
Course Instructor: Bime Mardonal. G
Instruction: Answer all questions. You are reminded of the necessity for good English and orderly of
your answers.
1. Let Answer the following with respect to .
(a) (5 Marks) Define the following:
(i) Limit point (ii) The closure of (iii) An interior point
(iv) Least upper bound (v) Greatest lower bound
(b) (5 Marks) When is said to be
(i) Bounded (ii) Open (iii) Closed (iv) An interval in
(v) Dense in
(c) (4 Marks) Define the following and give examples:
(i) A function (ii) An inductive set
(d) (3 Marks) Is it true that if is a limit point of then ?
Justify.
(e) i. (4 Marks) Is the set
bounded above(below)?
If so, find its supremum (infimum).
ii. (2 Marks) Is having a maximum element? Justify.
2. (4 Marks) Let be rational and irrational. Show that if , then is also irrational.
3. (a) (2 Marks) State the principle of Mathematical induction
(b) (4 Marks) Show that
is always a multiple of .
4. Find the domain and range, and plot the graph of the function determine by the given
formula:
(a) (4 Marks)
!
"
!
"
(b) (4 Marks) #
$% &
(c) (4 Marks) '
$
& %
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