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1/(1-x^2)
Limit of the function/ 1/(1-x^2)

Limit of the function 1/(1-x^2)

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The solution

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       1   
 lim ------
x->1+     2
     1 - x
lim⁡x→1+11−x2\lim_{x \to 1^+} \frac{1}{1 - x^{2}} 
Limit(1/(1 - x^2), x, 1)
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
-2.0-1.5-1.0-0.52.00.00.51.01.5-100100
Plot the graph
One‐sided limits [src] 
       1   
 lim ------
x->1+     2
     1 - x
lim⁡x→1+11−x2\lim_{x \to 1^+} \frac{1}{1 - x^{2}} 
-oo
−∞-\infty 
= -75.2508250825083
       1   
 lim ------
x->1-     2
     1 - x
lim⁡x→1−11−x2\lim_{x \to 1^-} \frac{1}{1 - x^{2}} 
oo
∞\infty 
= 75.7508305647841
= 75.7508305647841
Other limits x→0, -oo, +oo, 1
lim⁡x→1−11−x2=−∞\lim_{x \to 1^-} \frac{1}{1 - x^{2}} = -\infty
More at x→1 from the left
lim⁡x→1+11−x2=−∞\lim_{x \to 1^+} \frac{1}{1 - x^{2}} = -\infty
lim⁡x→∞11−x2=0\lim_{x \to \infty} \frac{1}{1 - x^{2}} = 0
More at x→oo
lim⁡x→0−11−x2=1\lim_{x \to 0^-} \frac{1}{1 - x^{2}} = 1
More at x→0 from the left
lim⁡x→0+11−x2=1\lim_{x \to 0^+} \frac{1}{1 - x^{2}} = 1
More at x→0 from the right
lim⁡x→−∞11−x2=0\lim_{x \to -\infty} \frac{1}{1 - x^{2}} = 0
More at x→-oo
Rapid solution [src] 
-oo
−∞-\infty
Expand and simplify
Numerical answer [src] 
-75.2508250825083
-75.2508250825083
The graph
Limit of the function 1/(1-x^2)
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