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Find the limit of $\left(1+\frac{3}{x}\right)^{2x}$ as $x$ approaches $\infty$

Step-by-step Solution

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$e^{6}$
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Step-by-step Solution

Problem to solve:

$\lim_{x\to\infty}\left(1+\frac{3}{x}\right)^{2x}$

Specify the solving method

1

Rewrite the limit using the identity: $a^x=e^{x\ln\left(a\right)}$

$\lim_{x\to\infty }\left(e^{2x\ln\left(1+\frac{3}{x}\right)}\right)$

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

$\lim_{x\to\infty }\left(e^{2x\ln\left(1+\frac{3}{x}\right)}\right)$

Learn how to solve limits to infinity problems step by step online. Find the limit of (1+3/x)^(2x) as x approaches \infty. Rewrite the limit using the identity: a^x=e^{x\ln\left(a\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. Rewrite the product inside the limit as a fraction.

$e^{6}$

$403.428793$
SnapXam A2

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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
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

Useful tips on how to improve your answer:

$\lim_{x\to\infty}\left(1+\frac{3}{x}\right)^{2x}$

Main topic:

Limits to Infinity

~ 0.19 s