EE004-3-1 Engineering Mathematics 1
Tutorials 1
Page 1 of 1
QUESTION 1
a) Apply L’Hopital’s rule to determine the following limit:
sin x  x
f ( x) f ' ( a )
lim
 ' , if f ( x)  0; g ( x)  0 and Dr  0
;Use
L’Hopital’s
rule
x 0
xa g ( x)
x2
g ( a)
lim
b) Test -the following series for convergence using the Comparison test:
1
3
5


 ......... , .
1.2.3 2.3.4 3.4.5
c) Test for the convergence of the series using the Leibnitz’ test:
1
1
1
1



 .....,
1. 2 3. 4 5 . 6 7 .8
QUESTION 2
3
a) Apply the first principles to determine the derivative of f ( x)  4 x at x = -2.
Use the first principle formula: f ' ( x)  lim
x 0
f ( x  x)  f ( x)
x
dy
ln 2t
if y 
, using quotient rule.
dt
t
du
du
v
u
d u
2
Use the quotient rule formula:
   dx 2 dx , v  0
dx  v 
v
b) Determine
c) The displacement, s, of a mass in a vibrating system is given by: s  (1  t )e t where  is
d 2s
ds
 2   2 s  0.
2
dt
dt
d (uv)
dv
du
u
v
Use the product rule formula :
dx
dx
dx
the natural frequency of vibration. Show that:
Level 1
Asia Pacific University of Technology & Innovation
201412