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Contests
National and Regional Contests
Bangladesh Contests
Bangladesh Mathematical Olympiad
2019 Bangladesh Mathematical Olympiad
6
6
Part of
2019 Bangladesh Mathematical Olympiad
Problems
(1)
BdMO National Higher Secondary 2019/6
Source: BdMO National Higher Secondary 2019/6
3/4/2019
When a function
f
(
x
)
f(x)
f
(
x
)
is differentiated
n
n
n
times ,the function we get id denoted
f
n
(
x
)
f^n(x)
f
n
(
x
)
.If
f
(
x
)
=
e
x
x
f(x)=\dfrac {e^x}{x}
f
(
x
)
=
x
e
x
.Find the value of
lim
n
→
∞
f
2
n
(
1
)
(
2
n
)
!
\lim_{n \to \infty} \dfrac {f^ {2n}(1)}{(2n)!}
n
→
∞
lim
(
2
n
)!
f
2
n
(
1
)
calculus
number theory