Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
Define
G
(
x
)
=
∫
2
g
(
x
)
1
t
2
d
t
G(x)=\int_{2}^{g(x)}\dfrac{1}{t^{2}}\,dt
G
(
x
)
=
∫
2
g
(
x
)
t
2
1
d
t
where
g
(
x
)
=
{
x
2
,
x
≤
1
sin
x
+
1
,
x
>
1
.
g(x)=\begin{cases}x^{2},&x\le 1\\ \sin x+1,&x>1\end{cases}.
g
(
x
)
=
{
x
2
,
sin
x
+
1
,
x
≤
1
x
>
1
.
Compute the left-hand and right-hand derivatives of
G
G
G
at
x
=
1
x=1
x
=
1
and state whether
G
G
G
is differentiable there.
Browse the problem library