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x/(1-x)

Limit of the function x/(1-x)

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The solution

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     /  x  \
 lim |-----|
x->1+\1 - x/
limx1+(xx+1)\lim_{x \to 1^+}\left(\frac{x}{- x + 1}\right)
Limit(x/(1 - x), x, 1)
Detail solution
Let's take the limit
limx1+(xx+1)\lim_{x \to 1^+}\left(\frac{x}{- x + 1}\right)
transform
limx1+(xx+1)\lim_{x \to 1^+}\left(\frac{x}{- x + 1}\right)
=
limx1+(xx+1)\lim_{x \to 1^+}\left(\frac{x}{- x + 1}\right)
=
limx1+(xx1)=\lim_{x \to 1^+}\left(- \frac{x}{x - 1}\right) =
(1)111+1=\left(-1\right) 1 \cdot \frac{1}{-1 + 1} =
= -oo

The final answer:
limx1+(xx+1)=\lim_{x \to 1^+}\left(\frac{x}{- x + 1}\right) = -\infty
Lopital's rule
There is no sense to apply Lopital's rule to this function since there is no indeterminateness of 0/0 or oo/oo type
The graph
-2.0-1.5-1.0-0.52.00.00.51.01.5-250250
Rapid solution [src]
-oo
-\infty
Other limits x→0, -oo, +oo, 1
limx1(xx+1)=\lim_{x \to 1^-}\left(\frac{x}{- x + 1}\right) = -\infty
More at x→1 from the left
limx1+(xx+1)=\lim_{x \to 1^+}\left(\frac{x}{- x + 1}\right) = -\infty
limx(xx+1)=1\lim_{x \to \infty}\left(\frac{x}{- x + 1}\right) = -1
More at x→oo
limx0(xx+1)=0\lim_{x \to 0^-}\left(\frac{x}{- x + 1}\right) = 0
More at x→0 from the left
limx0+(xx+1)=0\lim_{x \to 0^+}\left(\frac{x}{- x + 1}\right) = 0
More at x→0 from the right
limx(xx+1)=1\lim_{x \to -\infty}\left(\frac{x}{- x + 1}\right) = -1
More at x→-oo
One‐sided limits [src]
     /  x  \
 lim |-----|
x->1+\1 - x/
limx1+(xx+1)\lim_{x \to 1^+}\left(\frac{x}{- x + 1}\right)
-oo
-\infty
= -152.0
     /  x  \
 lim |-----|
x->1-\1 - x/
limx1(xx+1)\lim_{x \to 1^-}\left(\frac{x}{- x + 1}\right)
oo
\infty
= 150.0
= 150.0
Numerical answer [src]
-152.0
-152.0
The graph
Limit of the function x/(1-x)