# Step-by-step Solution

Go!
1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

## Step-by-step Solution

Problem to solve:

$\lim_{x\to\infty}x^{\frac{1}{x}}$

Solving method

Learn how to solve limits to infinity problems step by step online.

$\lim_{x\to\infty }\left(e^{\frac{1}{x}\ln\left(x\right)}\right)$

Learn how to solve limits to infinity problems step by step online. Find the limit (x)->(\infty)lim(x^(1/x)). Rewrite the limit using the identity: a^x=e^{x\ln\left(a\right)}. Multiplying the fraction by \ln\left(x\right). Apply the power rule of limits: \displaystyle{\lim_{x\to a}f(x)^{g(x)} = \lim_{x\to a}f(x)^{\displaystyle\lim_{x\to a}g(x)}}. The limit of a constant is just the constant.

$1$
$\lim_{x\to\infty}x^{\frac{1}{x}}$

### Main topic:

Limits to Infinity

~ 0.04 s