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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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     /     2\
 lim \2 - x /
x->2+
lim⁡x→2+(2−x2)\lim_{x \to 2^+}\left(2 - x^{2}\right) 
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
-4.0-3.0-2.0-1.04.00.01.02.03.0-2020
Plot the graph
Rapid solution [src] 
-2
−2-2
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→2−(2−x2)=−2\lim_{x \to 2^-}\left(2 - x^{2}\right) = -2
More at x→2 from the left
lim⁡x→2+(2−x2)=−2\lim_{x \to 2^+}\left(2 - x^{2}\right) = -2
lim⁡x→∞(2−x2)=−∞\lim_{x \to \infty}\left(2 - x^{2}\right) = -\infty
More at x→oo
lim⁡x→0−(2−x2)=2\lim_{x \to 0^-}\left(2 - x^{2}\right) = 2
More at x→0 from the left
lim⁡x→0+(2−x2)=2\lim_{x \to 0^+}\left(2 - x^{2}\right) = 2
More at x→0 from the right
lim⁡x→1−(2−x2)=1\lim_{x \to 1^-}\left(2 - x^{2}\right) = 1
More at x→1 from the left
lim⁡x→1+(2−x2)=1\lim_{x \to 1^+}\left(2 - x^{2}\right) = 1
More at x→1 from the right
lim⁡x→−∞(2−x2)=−∞\lim_{x \to -\infty}\left(2 - x^{2}\right) = -\infty
More at x→-oo
One‐sided limits [src] 
     /     2\
 lim \2 - x /
x->2+
lim⁡x→2+(2−x2)\lim_{x \to 2^+}\left(2 - x^{2}\right) 
-2
−2-2 
= -2.0
     /     2\
 lim \2 - x /
x->2-
lim⁡x→2−(2−x2)\lim_{x \to 2^-}\left(2 - x^{2}\right) 
-2
−2-2 
= -2.0
= -2.0
Numerical answer [src] 
-2.0
-2.0
The graph
Limit of the function 2-x^2
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