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x/(1-x)
Limit of the function/ x/(1-x)

Limit of the function x/(1-x)

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The solution

You have entered [src] 
     /  x  \
 lim |-----|
x->1+\1 - x/
lim⁡x→1+(x−x+1)\lim_{x \to 1^+}\left(\frac{x}{- x + 1}\right) 
Limit(x/(1 - x), x, 1)
Detail solution
Let's take the limit
lim⁡x→1+(x−x+1)\lim_{x \to 1^+}\left(\frac{x}{- x + 1}\right)
transform
lim⁡x→1+(x−x+1)\lim_{x \to 1^+}\left(\frac{x}{- x + 1}\right)
=
lim⁡x→1+(x−x+1)\lim_{x \to 1^+}\left(\frac{x}{- x + 1}\right)
=
lim⁡x→1+(−xx−1)=\lim_{x \to 1^+}\left(- \frac{x}{x - 1}\right) =
(−1)1⋅1−1+1=\left(-1\right) 1 \cdot \frac{1}{-1 + 1} = 
= -oo

The final answer:
lim⁡x→1+(x−x+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
Plot the graph
Rapid solution [src] 
-oo
−∞-\infty
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→1−(x−x+1)=−∞\lim_{x \to 1^-}\left(\frac{x}{- x + 1}\right) = -\infty
More at x→1 from the left
lim⁡x→1+(x−x+1)=−∞\lim_{x \to 1^+}\left(\frac{x}{- x + 1}\right) = -\infty
lim⁡x→∞(x−x+1)=−1\lim_{x \to \infty}\left(\frac{x}{- x + 1}\right) = -1
More at x→oo
lim⁡x→0−(x−x+1)=0\lim_{x \to 0^-}\left(\frac{x}{- x + 1}\right) = 0
More at x→0 from the left
lim⁡x→0+(x−x+1)=0\lim_{x \to 0^+}\left(\frac{x}{- x + 1}\right) = 0
More at x→0 from the right
lim⁡x→−∞(x−x+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/
lim⁡x→1+(x−x+1)\lim_{x \to 1^+}\left(\frac{x}{- x + 1}\right) 
-oo
−∞-\infty 
= -152.0
     /  x  \
 lim |-----|
x->1-\1 - x/
lim⁡x→1−(x−x+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)
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