Department of Mathematical Sciences, Faculty of Science
UNIVERSITI TEKNOLOGI MALAYSIA
SUBJECT: Mathematical Methods I (SSCM 1023)
SEMESTER I, 2015/16, Section: 04
Format of the assignment: (minimum 6 students per group) (Total Assignment & Quiz: 15%)
Type in Ms Word, Group members, Question, theory, calculation, answer and some diagram/graphs.
Please submit one hardcopy & softcopy (MsWord) of assignment for each group.
Email to : s.h.yeak@utm.my, office: C22-432
Group assignment (10%)
[quiz 1: 2%, quiz 2: 3%]
1. Find the derivative of the following functions.
(a)
y=sin(sinh x),
(b)
y=coth4 3x,
1
y
(c)
x  tanh x
2. Find the derivative of the following functions.
1  cosh x
y
(a)
.
1  cosh x
(b)
y  exp sinh x 2 .
1
y  sinh  
(c)
 x
3. Find the derivative of the following functions.
(a)
y=ln(tanh x).
(b)
y=tanh(ln x),
(c)
y=sinh(tanh x).


4. If x = cosh  and y = sinh , obtain dy/dx in terms of the parameter . Sketch the graphs of y and
dy/dx regarded as functions of .
5.
Use the definitions of cosh x and sinh x, prove that.
1
 cosh 2 x  sinh 2 x
cosh 2 x  sinh 2 x
Hence, or otherwise, show that
1
1
1
2
0 cosh 2 x  sinh 2 x dx  2 1  e 
6. Solve the below integral.
2
(a)
 sec h 2 xdx
sinh x
dx
2
x
7. Solve the below integral.
(a)
 cosh 2 x sinh 3xdx
(b)
 cosh
(b)
 cosh x cosh 3xdx
8. Solve the below integral.
3
(a)
 sinh  d
(b)
 cosh
3
 d
9. Solve the below integral.
x
(a)
 e cosh x dx
(b)
 sec h
3
x tanh x dx
10. Solve the below integral.
cosh x
(a)
 3 sinh x  2 cosh x dx
1
(b)
 cosh 2 x 1  tanh x  dx


1  tanh 2 x
 cosh 2 x . By mean of the substitution t = tanh x, or otherwise, find the
1  tanh 2 x
indefinite integral
 sec h 2 x dx
11. Show that
Questi
on No.
1
2
3
4
5
6
7
8
9
Name 1/2
Name 3/4
Name 5/6
Name 7/8
10
11