Analysis 1 (MATS2101)
BSc, Physics - PHYS
Semester: Resit
Level: 200
Year: 2016
REPUBLIC OF CAMEROON REPUBLIQUE DU CAMEROUN
Peace-Work-Fatherland Paix-Travail-Patrie
MINISTER OF HIGHER EDUCATION MINISTERE DE L’ENSEIGNMENT
THE UNIVERSITY OF BAMENDA
UNIVERSITE DE BAMENDA
FACULTY OF SCIENCE
FACULTE DES SCIENCE
P.O. Box 39 Bambili
Tell: (+237) 22 81 63 50
RESIT EXAMINATION 2015/2016 SESSION
DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE.
COURSE CODE: MATS2101 COURSE TITLE: Analysis I
Duration: 3 Hrs. Answer all questions.
1. Prove that (i) (B U C) n A = (B n A)U (C n A) (ii).(A U B)
c
= n(A
c
nB
c
). 8 pts
2. Let p and q be mathematical statements. Determine if the following statement is a contradiction or a tautology
(P => p) <=> ((p => q) <=> (~ q Vp)).10 pts
3. Define each of the following terms:(i) a function (ii)an injective function (iii) a surjective function which is
not bijective(w) a bijective function (v) a monotone increasing function . 8 pts
d. Give a justified example in each case, (i) an injective function which is not bijective (iv) a bijective function
(u) a monotone increasing function. 4 pts each
e. Evaluate the following limits
(i) lim
→∞
(ii)log
→∞
√
2
− −
√
+2
. 2+4 pts
(f) let {x
n
} and {y
n
}be sequences of real numbers.
(i) Prove that if{x
n
} converges to x, then /{x
n
}/ converges to /x/. 3 pts
(ii) Give a justified example of a sequence {x
n
} of real numbers which does not converge but /{x
n
}/ converges.
6 pts
(iii) prove that the sequence {x
n
} where x
n
=(-1)
n
is not a Cauchy sequence. 3 pts
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