SOALAN 1

PMM/JMSK/B5001/SESI JANUARI 2008

SOALAN 1

a) Buktikan koth 2 x 1 = kosekh 2 x.

( 5 markah ) Prove that coth 2 x 1 = cosekh 2 x.

( 5 marks )b) Lengkapkan jadual di bawah bagi persamaan . Seterusnya lakarkan graf yang terhasil bagi julat

Complete the table below for equation . Then, sketch the graph in the

range given as

x-6-4-20246

y

(10 markah )

( 10 marks )c) Dapatkan nilai bagi fungi hiperbola songsang berikut:

Find the value for the following inverse hiperbolic functions :

i)

ii)

iii)

( 6 markah )

( 6 marks )d) Tentukan nilai prinsip bagi fungsi trigonometri songsang berikut:

Find the principle value for the following inverse trigonometry functions, then sketch them:

i)

ii)

( 4 markah ) ( 4 marks )SOALAN 2

a)Cari bagi setiap fungsi yang berikut:

Find the derivative of each of the following functions:

i.y = sin-1 (x2 (1)

( 5 markah )

( 5 marks )ii

( 4 markah )

( 4 marks )b)Cari bagi fungsi berikut:

Find the derivative of the following functions:i.

e(3x kosh

( 3 markah )

( 3 marks )ii.

sinh(1

( 3 markah ) ( 3 marks )

iii.

(kos )

( 4 markah )

( 4 marks )c)Diberi , cari pada titik ((1,(1).

[Given , find at the point ((1,(1)}

( 6 markah )

( 6 marks )

SOALAN 3

a)Diberi dapatkan If

i.

ii.

(6 markah)

( 6 marks )b)Diberi dapatkan

Given

i.

ii.

iii.

iv

(12 markah)

( 12 marks )c)Jika z = f(x,y) dan , tentukan pembezaan keseluruhan, dz.

[ If z = f(x,y) and , determine the total differential, dz ]

(7 markah)

( 7 marks )SOALAN 4

a) Selesaikan setiap kamiran berikut: Solve the following integrals: i.

(5 markah )

( 5 marks )ii.

(4 markah )

( 4 marks )iii.

(4 markah )( 4 marks )b) Nilaikan kamiran berikut: Evaluate the following integrals: i.

(5 markah )( 5 marks )ii.

( 7 markah ) ( 7 marks )SOALAN 5

a) Selesaikan kamiran berikut menggunakan pecahan separa; Evaluate the following using integration by parts: i) dx(8 markah)

( 8 marks )ii) dx(8 markah) ( 8 marks )b) Selesaikan kamiran berikut dengan menggunakan kaedah kamiran bahagian demi bahagian:

Evaluate the following integrals by using partial fractions: i) dx(6 markah) ( 6 marks )ii) dx(3 markah) ( 3 marks )SOALAN 6

a)Bentukkan persamaan pembezaan bagi fungsi

Form a differential equation from the function .

( 4 markah )

( 4 marks )b)Dapatkan penyelesaian umum bagi persamaan berikut:

Find the general solutions of the following equations: i.

( 6 markah ) ( 6 marks )

ii.

( 7 markah ) ( 7 mark s)

iii.

( 8 markah )

( 8 marks )

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