Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
If
f
(
x
)
=
cot
−
1
(
3
x
−
x
3
1
−
3
x
2
)
f(x) = \cot^{-1} \left( \frac{3x - x^3}{1 - 3x^2} \right)
f
(
x
)
=
cot
−
1
(
1
−
3
x
2
3
x
−
x
3
)
and
g
(
x
)
=
cos
−
1
(
1
−
x
2
1
+
x
2
)
g(x) = \cos^{-1} \left( \frac{1 - x^2}{1 + x^2} \right)
g
(
x
)
=
cos
−
1
(
1
+
x
2
1
−
x
2
)
, then
lim
x
→
a
f
(
x
)
−
f
(
a
)
g
(
x
)
−
g
(
a
)
,
0
<
a
<
1
2
\lim_{x \rightarrow a} \frac{f(x) - f(a)}{g(x) - g(a)}, 0 < a < \frac{1}{2}
lim
x
→
a
g
(
x
)
−
g
(
a
)
f
(
x
)
−
f
(
a
)
,
0
<
a
<
2
1
is (a)
3
2
(
1
+
a
2
)
\frac{3}{2(1+a^2)}
2
(
1
+
a
2
)
3
(b)
3
2
(
1
+
x
2
)
\frac{3}{2(1+x^2)}
2
(
1
+
x
2
)
3
(c)
3
2
\frac{3}{2}
2
3
(d)
−
3
2
-\frac{3}{2}
−
2
3
Browse the problem library