Graphics Reference
In-Depth Information
Appendix 3
Questions for student investigation and discussion
Multiple-choice questions for student discussion
1
a
b
c
bc
ca
ab
is true:
A. always; B. sometimes; C. never.
2 If (
a
)
a
, must ((
a
)/
n
)
a
?A.Yes B.No
If ((
a
)/
n
)
a
, must (
a
)
a
?A.Yes B.No
3 The sequence (
a
) is bounded. Which of the following propositions
are suMcient to guarantee its convergence?
(i) (
a
)
0;
(ii) (
a
) is positive and bounded below;
(iii) (
a
) is bounded above and increasing;
(iv) for all
n
,
a
a
;
(v) noneof theabov.
4 Between two rationals there is an irrational. Between two
irrationals threis a rational. So therationals and theirrationals
alternate on the line.
A. This is a valid argument.
B. The result is true but the argument is invalid.
C. The result is false.
5 Trueor fals?
Whatever the values of
a
or
b
, thest [
a
,
b
]
Q contains its own
supremum and infimum.
Whatever the values of
a
or
b
, thest (
a
,
b
)
Q never contains its
own supremum or infimum.
