MathDB
Problems
Contests
National and Regional Contests
India Contests
India LIMIT
2020 LIMIT
2020 LIMIT Category 2
16
16
Part of
2020 LIMIT Category 2
Problems
(1)
lim frac{f^{(2n)}1}{(2n)!}, f(x)=\frac{e^x}{x}
Source: LIMIT 2020 Cat 2 Objective P16
6/9/2020
The
n
t
h
n^{th}
n
t
h
derivative of a function
f
(
x
)
f(x)
f
(
x
)
(if it exists) is denoted by
f
(
n
)
(
x
)
f^{(n)}(x)
f
(
n
)
(
x
)
. Let
f
(
x
)
=
e
x
x
f(x)=\frac{e^x}{x}
f
(
x
)
=
x
e
x
. Suppose
f
f
f
is differentiable infinitely many times in
(
0
,
∞
)
(0,\infty)
(
0
,
∞
)
. Then find
lim
n
→
∞
f
(
2
n
)
1
(
2
n
)
!
\lim_{n \to \infty}\frac{f^{(2n)}1}{(2n)!}
lim
n
→
∞
(
2
n
)!
f
(
2
n
)
1
limit
derivative
calculus