QMS702 – Review Questions (Final Exam)
Question 1. Given that the demand and supply functions are
p = d ( x) = −5 x + 40 and p = s( x) = x 2 + 3x + 20, respectively. Determine
the consumer's surplus and the producer's surplus if the market price is
set at the equilibrium price.
Question 2. The demand function for a certain brand of compact disc is
p 2 = −0.01x 2 − 0.2 x + 8.76
where p is the unit price in dollars and x is the quantity demanded each
week, measured in units of a thousand. Compute the elasticity of
demand and determine whether the demand is elastic when p = 2 .4 .
Question 3. Find
(a) 1
(b) 0
x 4 −1
2
x → − 1 2 x + 3 x +1
lim
(c)
∞
(d) DNE
x
2e
Question 4. If f ( x) = e , find f ' (0).
1
(e) 4
dy
Question 5. Find
dx
2
8
if y = x ( x + 1) + ln( e
2x
+ 1).
Question 6. Evaluate the integral:
2
255
3
(
x
+
1
)
(
x
+ 2 x)dx

1
x
|
e
− 1 | dx
Question 7. Evaluate 
−1
3
2
Question 8. Consider the function f (x) = 5x + 2x − 3x.
(1) Find the local minimum and maximum.
(2) Find the intervals on which the graph of f (x) is concave up/down.
Find its inflection points if exist.
2
Question 9. Given that the marginal cost for a product is
C ' ( x ) = 5 x + 10, and the cost of producing 20 units is $1,500.
(a)
(b)
Find the fixed cost.
Find the total cost of producing 30 units.
Question 10. Suppose that monthly records show that the rate of change
of the revenue (i.e., the marginal revenue) for a product is
R' ( x) = 3 2 x + 25 , where x is the number of units and the cost is in
dollars. What would be the total revenue of selling 300 items per month?
Question 11. What is the domain of y =
(a)
( −∞ , 2 )
(b)
(c)
( −∞ , ln 2 ) ∪ (ln 2 , 2 )
(d)
x 2 +3 x + 2
e2 x −4
+ ln(4 − 2 x) ?
( −∞ , ln 4 ) ∪ (ln 4 , 2 )
( −∞ , ln 2 ) ∪ (ln 2 , 2 ]
Question 12. A piece of wire 100cm long is cut into two pieces. One
piece will be bent to form a circle, and the other will be bent to form a
square. Find the radius of the circle and the size of the square so that the
total area is minimum.
3
∞
Question 13. Determine if 
4
1
x3
dx is convergent. If so, find its value.
Question 14. Consider the following probability density function of a
continuous random variable of X:
𝑓 𝑥 = 𝑘√𝑥, 0 ≤ 𝑥 ≤ 1
0,
𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
Find (1) k
(2) the expected value of X
(3) the standard deviation of X.
4