Dawson College - Winter 2008
Mathematics Department
Final Examination
Calculus 2 (NYB commerce)
1. (4 points) Find
(
)
xf
given
( )
3
2
3
4
f x x x
x
′= − − and
(
)
71 −=f
.
2. (6 points) Use the definition (Riemann Sum) to evaluate the definite integral
( )
∫
+−
5
0
2
32 dxxx .
( ) ( )( )
2
1 1
1 1 2 1
and
2 6
n n
k k
n n n n n
k k
= =
+ + +
= =
∑ ∑
3.
(10 points
) Find the indefinite integral.
(a)
(
)
∫
++
dxee
xx 1212
cos10
(b)
∫
−dxxx 14
4.
(10 points
) Find the indefinite integral.
(a)
(
)
∫
dxxx 3ln (b)
( )
( )
∫++−
++
dx
xxx
xx
11
225
2
2
5. (5 points) The weekly marginal cost of a product is given by
(
)
202.00015.0
2
+−=
′xxxC
where
(
)
xC
′
is measured in dollars per unit and x is the number of units produced per week.
If the fixed costs are $1200 , find the total weekly cost of production of 200 units.
6. (6 points) Find the average value of the function
(
)
(
)
1
sin 4
x
f x x e
+
= − − over
[
]
1,2
−
.
7. (6 points) Consider the functions
(
)
561 −+= xxf and
(
)
1+= xxg
. Find the area of the region completely enclosed
by the graphs of f and g .
8.
(6 points
) The demand function for a product is given by
(
)
2
0.01 0.7 110
p D x x x= = − − + , and the supply function
is given by
(
)
2
0.05 0.7 56
p S x x x
= = − +
.
(a)
Find the market equilibrium price.
(b)
Find the producers’ surplus at the equilibrium price.
