Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
Which of the following is a required hypothesis for applying the Integral Test to the series
∑
n
=
1
∞
f
(
n
)
\displaystyle \sum_{n=1}^{\infty} f(n)
n
=
1
∑
∞
f
(
n
)
? a)
lim
x
→
∞
f
(
x
)
=
0
\displaystyle \lim_{x\to\infty} f(x)=0
x
→
∞
lim
f
(
x
)
=
0
b)
∫
1
∞
f
(
x
)
d
x
converges
\displaystyle \int_{1}^{\infty} f(x)\,dx \text{ converges}
∫
1
∞
f
(
x
)
d
x
converges
c)
f
(
x
)
is positive for
x
≥
1
f(x)\text{ is positive for }x\ge 1
f
(
x
)
is positive for
x
≥
1
d)
f
(
x
)
has only finitely many discontinuities on
[
1
,
∞
)
f(x)\text{ has only finitely many discontinuities on }[1,\infty)
f
(
x
)
has only finitely many discontinuities on
[
1
,
∞
)
Browse the problem library