Answer to Question #60658 in Real Analysis for esita

Question

Which of the following statements are true or false? Give reasons for your answers. (10)
a) The singleton set {x} for any x ∈ R is an open set.
(b) The series is − + − +L
7
1
5
1
3
1
1 is a convergent series.
c) The function



=
+ ≠
=
−
,1 when 0
, when 0
( )
x
e e x
f x
x x
is continuous on ]1,0[ .
d) The function f defined by f (x) = | x − |2 ∀x ∈ R has a critical point at x = 2 .
e) If a function has finitely many points of discontinuities, then the function is not
integrable.