A person with $14,000 is trying to decide whether to purchase a car now, or to invest the money at 6.5 % compounded semiannually and then buy a more expensive car. How much will be available for the purchase of a car at the end of 3 years?
A person with $14,000 is trying to decide whether to purchase a car now, or to invest the money at 6.5 % compounded semiannually and then buy a more expensive car. How much will be available for the purchase of a car at the end of 3 years?
Solution Summary: The author calculates the amount available at the end of 3 years to purchase a car. The interest rate is represented by the formula, i=rm.
A person with
$14,000
is trying to decide whether to purchase a car now, or to invest the money at
6.5
%
compounded semiannually and then buy a more expensive car. How much will be available for the purchase of a car at the end of
3
years?
Keity
x२
1. (i)
Identify which of the following subsets of R2 are open and which
are not.
(a)
A = (2,4) x (1, 2),
(b)
B = (2,4) x {1,2},
(c)
C = (2,4) x R.
Provide a sketch and a brief explanation to each of your answers.
[6 Marks]
(ii)
Give an example of a bounded set in R2 which is not open.
[2 Marks]
(iii)
Give an example of an open set in R2 which is not bounded.
[2 Marks
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
Chapter 3 Solutions
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences Plus NEW MyLab Math with Pearson eText -- Access Card Package (13th Edition)
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
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