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# Find the limit of $x\frac{\ln\left(x\right)}{x-1}$ as $x$ approaches $1$

## Step-by-step Solution

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ln
log
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sin
cos
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acos
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sinh
cosh
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asinh
acosh
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Solving: $\lim_{x\to1}\left(x\frac{\ln\left(x\right)}{x-1}\right)$

### Videos

$1$
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## Step-by-step Solution

Problem to solve:

$\lim_{x\to1}\left(x\frac{\ln\left(x\right)}{x-1}\right)$

Choose the solving method

1

Multiplying the fraction by $x$

$\lim_{x\to1}\left(\frac{x\ln\left(x\right)}{x-1}\right)$

Learn how to solve limits by direct substitution problems step by step online.

$\lim_{x\to1}\left(\frac{x\ln\left(x\right)}{x-1}\right)$

Learn how to solve limits by direct substitution problems step by step online. Find the limit of x(ln(x)/(x-1) as x approaches 1. Multiplying the fraction by x. If we directly evaluate the limit \lim_{x\to 1}\left(\frac{x\ln\left(x\right)}{x-1}\right) as x tends to 1, we can see that it gives us an indeterminate form. We can solve this limit by applying L'Hôpital's rule, which consists of calculating the derivative of both the numerator and the denominator separately. After deriving both the numerator and denominator, the limit results in.

$1$
SnapXam A2

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1
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5
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7
8
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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

### Tips on how to improve your answer:

$\lim_{x\to1}\left(x\frac{\ln\left(x\right)}{x-1}\right)$

### Main topic:

Limits by direct substitution

~ 0.05 s