PMB 3004: Calculus

Tutorial 2

1. Change the following improper rational functions to the proper rational functions:

a) ( x3 + 5x

2 – x – 6) / (x-1)

b) (4x3 – 2x

2 - x + 3 ) / x -2

c) (4x3 + 6x

2 + 5x +3) / (2x-1)

d) (x3 + 5x

2 - 2x -1) / (x+3)

2. Simplify the following expressions:

3 7

1.5

1/ 2

3 1

3 2

)2 3

)5

4 3)

2

a e e

eb

e

e ec

e e

d) 2 2( 1) (1 ) x x x x xe e e e e

e) 2

1

x x

x

x

e ee

e

f) 2 2(1 ) x xe e

3. Simplify the following expressions:

3

9

) ln 2ln 3ln

1) ln ln

2

) log 100 log 10 log 5

10ln ln ln)

ln ln

a a a

a x x x

b t t

c

x x xd

x x

e) 2 2 24log 2logrs t r st

f) 2 3

2 6

1 1log log

2 3

x x

y y

4. Solve the following equations:

PMB/ NS/Jan 09

a) 312525 x

b) 325 x

c) 16

12 1 x

d) 42ln xe

e) 2 3x xe e

f) 1

21

xe

g) 610 30 x

h) 2

10log 4 2x

i) 2ln(3 5) 4 t

j) log x log 2 1

k) 3 43ln( ) 9 xe

l) 2log(x 2) log(2x 5)

m) 2log(x 6) log(x 1) 1

n) ln xe 2x 3