Function Properties Integral Definition (Jee Ma… | ExamDuo
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Definite Integrals and Reduction
Medium
Function Properties Integral Definition
Let
f
:
[
0
,
∞
)
→
[
0
,
∞
)
be defined as
f
(
x
)
=
x
∫
0
[
y
]
d
y
where
[
x
]
is the greatest integer less than or equal to
x
. Which of the following is true?
Ask about this question
SELECT ONE OPTION
A
f is continuous everywhere except at the integer points in
[
0
,
∞
)
.
B
f
is continuous at every point in
[
0
,
∞
)
and differentiable except at the integer points.
C
f
is both continuous and differentiable except at the integer points in
[
0
,
∞
)
.
D
f is differentiable at every point in
[
0
,
∞
)
.
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