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