Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
For the function
f
(
x
)
=
x
cos
1
x
,
x
≥
1
f(x) = x \cos \frac{1}{x}, x \ge 1
f
(
x
)
=
x
cos
x
1
,
x
≥
1
, a. for atleast one
x
x
x
in the interval
[
1
,
∞
)
[1, \infty)
[
1
,
∞
)
,
f
(
x
+
2
)
−
f
(
x
)
<
2
f(x+2) - f(x) < 2
f
(
x
+
2
)
−
f
(
x
)
<
2
b.
lim
x
→
∞
f
′
(
x
)
=
1
\lim_{x \to \infty} f'(x) = 1
lim
x
→
∞
f
′
(
x
)
=
1
c. for all
x
x
x
in the interval
[
1
,
∞
)
[1, \infty)
[
1
,
∞
)
,
f
(
x
+
2
)
−
f
(
x
)
>
2
f(x+2) - f(x) > 2
f
(
x
+
2
)
−
f
(
x
)
>
2
d.
f
′
(
x
)
f'(x)
f
′
(
x
)
is strictly decreasing in the interval
[
1
,
∞
)
[1, \infty)
[
1
,
∞
)
Browse the problem library