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

Limit of the function (-2+x)^(-2)

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The solution

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         1    
 lim ---------
x->2+        2
     (-2 + x)
lim⁡x→2+1(x−2)2\lim_{x \to 2^+} \frac{1}{\left(x - 2\right)^{2}} 
Limit((-2 + x)^(-2), x, 2)
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
-4.0-3.0-2.0-1.04.00.01.02.03.0025000
Plot the graph
One‐sided limits [src] 
         1    
 lim ---------
x->2+        2
     (-2 + x)
lim⁡x→2+1(x−2)2\lim_{x \to 2^+} \frac{1}{\left(x - 2\right)^{2}} 
oo
∞\infty 
= 22801.0
         1    
 lim ---------
x->2-        2
     (-2 + x)
lim⁡x→2−1(x−2)2\lim_{x \to 2^-} \frac{1}{\left(x - 2\right)^{2}} 
oo
∞\infty 
= 22801.0
= 22801.0
Rapid solution [src] 
oo
∞\infty
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→2−1(x−2)2=∞\lim_{x \to 2^-} \frac{1}{\left(x - 2\right)^{2}} = \infty
More at x→2 from the left
lim⁡x→2+1(x−2)2=∞\lim_{x \to 2^+} \frac{1}{\left(x - 2\right)^{2}} = \infty
lim⁡x→∞1(x−2)2=0\lim_{x \to \infty} \frac{1}{\left(x - 2\right)^{2}} = 0
More at x→oo
lim⁡x→0−1(x−2)2=14\lim_{x \to 0^-} \frac{1}{\left(x - 2\right)^{2}} = \frac{1}{4}
More at x→0 from the left
lim⁡x→0+1(x−2)2=14\lim_{x \to 0^+} \frac{1}{\left(x - 2\right)^{2}} = \frac{1}{4}
More at x→0 from the right
lim⁡x→1−1(x−2)2=1\lim_{x \to 1^-} \frac{1}{\left(x - 2\right)^{2}} = 1
More at x→1 from the left
lim⁡x→1+1(x−2)2=1\lim_{x \to 1^+} \frac{1}{\left(x - 2\right)^{2}} = 1
More at x→1 from the right
lim⁡x→−∞1(x−2)2=0\lim_{x \to -\infty} \frac{1}{\left(x - 2\right)^{2}} = 0
More at x→-oo
Numerical answer [src] 
22801.0
22801.0
The graph
Limit of the function (-2+x)^(-2)
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