Supply and demand. At a price of $3 .20 per bushel, the supply of corn is 9,800 million bushels and the demand is 9,200 million bushels. At a price of $2 .95 per bushel, the supply is 9,300 million bushels and the demand is 9,700 million bushels. (A) Find a price-supply equation of the form p = m x + b . (B) Find a price-demand equation of the form p = m x + b . (C) Find the equilibrium point. (D) Graph the price-supply equation, price-demand equation, and equilibrium point in the same coordinate system .
Supply and demand. At a price of $3 .20 per bushel, the supply of corn is 9,800 million bushels and the demand is 9,200 million bushels. At a price of $2 .95 per bushel, the supply is 9,300 million bushels and the demand is 9,700 million bushels. (A) Find a price-supply equation of the form p = m x + b . (B) Find a price-demand equation of the form p = m x + b . (C) Find the equilibrium point. (D) Graph the price-supply equation, price-demand equation, and equilibrium point in the same coordinate system .
Supply and demand. At a price of
$3
.20
per bushel, the supply of corn is 9,800 million bushels and the demand is 9,200 million bushels. At a price of
$2
.95
per bushel, the supply is 9,300 million bushels and the demand is 9,700 million bushels.
(A) Find a price-supply equation of the form
p
=
m
x
+
b
.
(B) Find a price-demand equation of the form
p
=
m
x
+
b
.
(C) Find the equilibrium point.
(D) Graph the price-supply equation, price-demand equation, and equilibrium point in the
same coordinate system.
System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.
2.
(i)
Which of the following statements are true? Construct coun-
terexamples for those that are false.
(a)
sequence.
Every bounded sequence (x(n)) nEN C RN has a convergent sub-
(b)
(c)
(d)
Every sequence (x(n)) nEN C RN has a convergent subsequence.
Every convergent sequence (x(n)) nEN C RN is bounded.
Every bounded sequence (x(n)) EN CRN converges.
nЄN
(e)
If a sequence (xn)nEN C RN has a convergent subsequence, then
(xn)nEN is convergent.
[10 Marks]
(ii)
Give an example of a sequence (x(n))nEN CR2 which is located on
the parabola x2 = x², contains infinitely many different points and converges
to the limit x = (2,4).
[5 Marks]
2.
(i) What does it mean to say that a sequence (x(n)) nEN CR2
converges to the limit x E R²?
[1 Mark]
(ii) Prove that if a set ECR2 is closed then every convergent
sequence (x(n))nen in E has its limit in E, that is
(x(n)) CE and x() x
x = E.
[5 Marks]
(iii)
which is located on the parabola x2 = = x
x4, contains a subsequence that
Give an example of an unbounded sequence (r(n)) nEN CR2
(2, 16) and such that x(i)
converges to the limit x = (2, 16) and such that x(i)
#
x() for any i j.
[4 Marks
1. (i)
which are not.
Identify which of the following subsets of R2 are open and
(a)
A = (1, 3) x (1,2)
(b)
B = (1,3) x {1,2}
(c)
C = AUB
(ii)
Provide a sketch and a brief explanation to each of your answers.
[6 Marks]
Give an example of a bounded set in R2 which is not open.
(iii)
[2 Marks]
Give an example of an open set in R2 which is not bounded.
[2 Marks]
Chapter 1 Solutions
Pearson eText for Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences -- Instant Access (Pearson+)
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