Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
Prove that for any positive integer
n
n
n
, the following limit holds:
lim
h
→
0
(
x
+
h
)
n
−
x
n
h
=
n
x
n
−
1
.
\lim_{h\to 0}\frac{(x+h)^n-x^n}{h}=n\,x^{\,n-1}.
h
→
0
lim
h
(
x
+
h
)
n
−
x
n
=
n
x
n
−
1
.
Browse the problem library