1. PMB 3004: Calculus
Tutorial 2
1. Change the following improper rational functions to the proper rational functions:
a) ( x3 + 5x2 – x – 6) / (x-1)
b) (4x3 – 2x2 - x + 3 ) / x -2
c) (4x3 + 6x2 + 5x +3) / (2x-1)
d) (x3 + 5x2 - 2x -1) / (x+3)
2. Simplify the following expressions:
a )2e3 3e 7
d) e2 x (e2 x  e x  1)  e x (1  e x )
e 1.5
b) e2 x  e x
5e1/ 2 e) x
 1  ex
e
4e3 3e 1 f) e2 x  (1  e x )2
c)
2 e 3 e 2
3. Simplify the following expressions:
a ) ln x  2 ln x  3ln x
e) 4log rs 2 t  2log r 2 st 2
1
b) ln t  ln t 1 x2 1 x3
2 f) log 2  log 6
2 y 3 y
c) log a 100  log a 10  log a 5
10 ln x  ln x  ln x 3
d)
ln x 9  ln x
4. Solve the following equations:

2. a) 25x  1253 h) log10 4 x 2  2
b) x 5  32 i) 2ln(3t  5)  4
1
c) 2 x 1  j) log x  log 2  1
16
k) 3ln(e3 x 4 )  9
d) e ln 2 x  4
e) e2 x  3e x l) 2log(x  2)  log(2x  5)
f)
1
2 m) log(x 2  6)  log(x  1)  1
e 1
x
n) eln x  2x  3
g) 10 x 6  30
PMB/ NS/Jan 09