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# Find the limit $\lim_{x\to0}\left(\left(x+\sin\left(x\right)\right)^{\tan\left(x\right)}\right)$

## Step-by-step Solution

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## Step-by-step Solution

Problem to solve:

$\lim_{x\to0}\left(x+\sin\left(x\right)\right)^{\tan\left(x\right)}$

Specify the solving method

1

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

$\lim_{x\to0}\left(e^{\tan\left(x\right)\ln\left(x+\sin\left(x\right)\right)}\right)$

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

$\lim_{x\to0}\left(e^{\tan\left(x\right)\ln\left(x+\sin\left(x\right)\right)}\right)$

Learn how to solve limits of exponential functions problems step by step online. Find the limit (x)->(0)lim((x+sin(x))^tan(x)). 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.

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### Explore different ways to solve this problem

Limits by direct substitutionLimits by L'Hôpital's ruleLimits by factoringLimits by rationalizing
SnapXam A2

### beta Got another answer? Verify it!

Go!
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0
a
b
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n
u
v
w
x
y
z
.
(◻)
+
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◻/◻
/
÷
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

$\lim_{x\to0}\left(x+\sin\left(x\right)\right)^{\tan\left(x\right)}$

### Main topic:

Limits of Exponential Functions

12. See formulas

~ 0.37 s