200238 Mathematics for Engineering 2 - Sample Class Test 2
Purpose: This class test is designed to determine your knowledge and understanding of the topics
presented in weeks 7-12, i.e. the content covered in Laplace transforms, multivariable calculus and
Sample final examination questions for Class Test 3 (2)
Question 3
x2
does not exist.
2
2
( x , y ) (0,0) 2 x + y
lim
a)
Show that
b)
Given z = xy , x = 2t 1, y = 3t + 4, use the chain rule to find
dz
as a function
dt
of t.
c)
A marble is set on the surfa
Sample final examination questions for Class Test 3
Question 3
a)
Show that the function
x4 y 4
f ( x) = x 2 + y 2
0
is continuous at (0, 0).
( x, y ) (0, 0)
( x, y ) = (0, 0)
b)
Given z = euv and u = x3 , v = x y 2 , use the chain rule to determine
c)
z
School of Computing and Mathematics
200238 Maths for Engineers 2
Class Test 2 Solutions
Question 1
(8 marks)
Find the general solution of y 2 y y 12e3 x .
3 2 2 ( 2 2 1) ( 1) 2 0
0, 1, 1
yh c1e0 x c2 e x c3 xe x c1 c2 e x c3 xe x
y p Ae3 x , y 3 Ae3 x ,
Sample final examination questions
Question 2
a)
Find the general solution of the differential equation y 3 y + 3 y y = e 2 x + 1.
(i)
Show that the differential equation y + 2 y 8 y = 0 can be written as the
order system of equations
0 1
y =
y.
8 2
School of Computing and Mathematics
200238 Maths for Engineers 2
Class Test 2
NAME:STUDENT ID:
TUTORIAL: Thursday 2pm
Friday
10 am
3pm
12noon
4pm
1pm
Time allowed: 40 minutes.
Total Marks: 30 marks.
(circle one)
Show all working in the space provided. So
Composites
Sandwich panel construction
Nanocomposites
The faces cannot buckle
well supported by the core
core material obtained in many different strengths
common core materials construction are foam, balsa & honeycomb
Nanocomposites
Nanocomposites
C
Composites
EffectoffiberOrientation
Tapes containing aligned fibers can Tapes containing aligned fibers can
be joined to produce a multibe joined with different
layered unidirectional
orientations to produce a
composite structure
quasi-isotropic composite
Composites
EffectoffiberOrientation
Maximum strength is obtained
when long fibers are
oriented parallel to the
applied load.
Effect of fiber orientation on tensile strength of E-glass
fiber-reinforced epoxy composite.
TypicalPropertydifferencesCFRP
Epoxy