Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Lebl-Basic-Analysis-I
· Problem 4.3.5
The Derivative
Mathematics · taylor-remainder-limit
Problem
If
f
:
[
a
,
b
]
→
R
f : [a,b] \to \mathbb{R}
f
:
[
a
,
b
]
→
R
has
n
+
1
n+1
n
+
1
continuous derivatives and
x
0
∈
[
a
,
b
]
x_0 \in [a,b]
x
0
∈
[
a
,
b
]
, prove
lim
x
→
x
0
R
n
x
0
(
x
)
(
x
−
x
0
)
n
=
0
\displaystyle\lim_{x \to x_0} \frac{R_n^{x_0}(x)}{(x-x_0)^n} = 0
x
→
x
0
lim
(
x
−
x
0
)
n
R
n
x
0
(
x
)
=
0
.
Related theory
Limit Superior And Limit Inferior
Browse the problem library