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# Find the limit $\lim_{x\to0}\left(\left(1+\frac{5x}{2}\right)^{\frac{3}{x}}\right)$

## Step-by-step Solution

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###  Videos

$1808.042414$
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##  Step-by-step Solution 

Problem to solve:

$\lim_{x\to0}\left(\left(1+\frac{5x}{2}\right)^{\frac{3}{x}}\right)$

Specify the solving method

1

Combine $1+\frac{5x}{2}$ in a single fraction

$\lim_{x\to0}\left(\left(\frac{5x+2}{2}\right)^{\frac{3}{x}}\right)$

Learn how to solve limits of exponential functions problems step by step online.

$\lim_{x\to0}\left(\left(\frac{5x+2}{2}\right)^{\frac{3}{x}}\right)$

Learn how to solve limits of exponential functions problems step by step online. Find the limit (x)->(0)lim((1+(5x)/2)^(3/x)). Combine 1+\frac{5x}{2} in a single fraction. Rewrite the limit using the identity: a^x=e^{x\ln\left(a\right)}. Multiplying the fraction by \ln\left(\frac{5x+2}{2}\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)}}.

$1808.042414$

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Limits by Direct SubstitutionLimits by L'Hôpital's ruleLimits by factoringLimits by rationalizing

SnapXam A2

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1
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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
|◻|
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

### Main topic:

Limits of Exponential Functions

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