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Find the limit $\lim_{x\to1}\left(\left(1+3\ln\left(x\right)\right)^{\frac{1}{\sin\left(1-x\right)}}\right)$

Step-by-step Solution

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Final Answer

$\frac{1}{e^{3}}$
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Step-by-step Solution

Problem to solve:

$\lim_{x\to\:1}\left(1+3\cdot\:lnx\right)^{\left(\frac{1}{sen\:\left(1-x\right)}\right)}$

Specify the solving method

1

Evaluate the limit $\lim_{x\to1}\left(\left(1+3\ln\left(x\right)\right)^{\frac{1}{\sin\left(1-x\right)}}\right)$ by replacing all occurrences of $x$ by $1$

$\left(1+3\ln\left(1\right)\right)^{\frac{1}{\sin\left(1-1\cdot 1\right)}}$

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

$\left(1+3\ln\left(1\right)\right)^{\frac{1}{\sin\left(1-1\cdot 1\right)}}$

Unlock the first 3 steps of this solution!

Learn how to solve limits of exponential functions problems step by step online. Find the limit (x)->(1)lim((1+3ln(x))^(1/(sin(1-x))). Evaluate the limit \lim_{x\to1}\left(\left(1+3\ln\left(x\right)\right)^{\frac{1}{\sin\left(1-x\right)}}\right) by replacing all occurrences of x by 1. Simplifying, we get. Apply the formula for limits that result in the indeterminate form 1^{\infty}, which is as follows: \lim_{x\to a}f(x)^{g(x)}=\lim_{x\to a}e^{\left[g(x)\cdot\left(f(x)-1\right)\right]}. Multiplying the fraction by 3\ln\left(x\right).

Final Answer

$\frac{1}{e^{3}}$

Numeric Answer

$0.049787$
SnapXam A2
Answer Assistant

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Got another answer? Verify it!

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
|◻|
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

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