Tutorial8.pdf

UNIVERSITI PUTRA MALAYSIA

FAKULTI SAINS


MTH 3004 PENGENALAN KEPADA MATEMATIK EKONOMI DAN PERNIAGAAN
Tutorial 8
1. Use differentials and R=300 x + 50 x2 − x 3 to approximate the change in revenue R (in
RM) from selling x kg if the number of kg increases from 10 to .

2. Use differentials and C=250 + 0 . 30 x to approximate the change in cost C (in RM) to
produce x kg of candy if the number of kg of candy increases from 10 kg to kg.

3. Find the indefinite integral
(2x+ 1)( 3 x − 2 ) 5x4− 7 x 2 + 9
a) dx b) dx
∫ 6 ∫ x2
2
4 x
c) x22 x 3 − 5 dx d) dx
∫( ) ∫ 2
(4x3 − 3 )

dy
4. If =x2 −4 x + 1 and y (3) = 8 , find y.
dx
dc
5. The marginal cost function for a manufacturer’s product is given by =2q + q3 + e q ,
dq
where c is in RM. Find the cost function if fixed costs are RM100.

6. Determine
4x
1 5 4 e
a) x( x2 −1) dx b) dx
∫0 ∫0 4

dc 2
7. A manufacturer’s marginal cost function is =( − 20 ) , where c is the total
dq
cost (in RM) of producing q units of a product. If the manufacturer increases output
from 50 units to 100 units, determine the change in total cost.

8. Sketch and find the