Mathematical Methods (MATS2108)
Geology, Mining and Environmental Science - GENV
Semester: Resit
Level: 200
Year: 2019
REPUBLIC OF CAMEROON
The UNIVERSITY OF BAMENDA
Facility:
Science
Department:
BIO CHEM
Lec
turer(s): Chi
i
Walter Ndifon
Course Code: MAT2108
Course
Title: MATHEMATICS for
BIO
RESIT
Date: 35/072019 Hall:
Time
3 hour
(
12,30.12.80)
Answer all questions. Each question carries equal marks
QUESTION 1 (17.5 marks)
(a) Define the following teams
(i) Function (ii) Injective functions (iii) Surjective functions
(b) State the following Theorems
(i) Maximum and Minimum Value Theorem
(ii) Taylor Theorem
(iii) Langrage Remainder Theorem.
QUESTION 2 (17.5 marks)
a. Evaluate the following limits
i)
lim
→
−
ii)
lim
→
√
− 1
iii)
lim
→
1 +
iv)
lim
→
1 +
v)
lim
→
√
√
QUESTION 3 (17.5 marks)
(a) Define derivative of a function at a point and hence compute the
derivative of a function F(x)= 3x
3
+ 2x-I at x = 10
b. By using the first principle solve the following functions
(i).f(x)= sinx. (ii) f(x)=
(iii) f(x)= 7x
2
+ 5x+ 2
QUESTION 4 (17.5 marks)
a. Define integration of a function and hence solve the following integrals
i)
2
√
ii)
www.schoolfaqs.net
b. State fundament theorem of calculus and hence
(i) find the area bounded by the curve x= y
2
and x = 2-y
2
on the closed
interval -1,1.
Instruction:- Answer true or false.
i. P(A/B)= 0.6 and P(A) = 0.2, hence A and B are independent.
TRUE FALSE
ii. The sum of the probabilities, Px
1,
Px
2
. ............. Pxm is always greater
than one TRUE ................................................... FALSE
iii. Binomial and normal distributions are examples of discrete probability
distributions. TRUE FALSE
iv. If the sample size is small the unbiased mean is U while the unbiased
variance S =
∑
TRUE or FALSE.
GOOD LUCK
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