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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+(x2+2)\lim_{x \to 2^+}\left(x^{2} + 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
-4.0-3.0-2.0-1.04.00.01.02.03.0020
Plot the graph
One‐sided limits [src] 
     /     2\
 lim \2 + x /
x->2+
lim⁡x→2+(x2+2)\lim_{x \to 2^+}\left(x^{2} + 2\right) 
6
66 
= 6.0
     /     2\
 lim \2 + x /
x->2-
lim⁡x→2−(x2+2)\lim_{x \to 2^-}\left(x^{2} + 2\right) 
6
66 
= 6.0
= 6.0
Other limits x→0, -oo, +oo, 1
lim⁡x→2−(x2+2)=6\lim_{x \to 2^-}\left(x^{2} + 2\right) = 6
More at x→2 from the left
lim⁡x→2+(x2+2)=6\lim_{x \to 2^+}\left(x^{2} + 2\right) = 6
lim⁡x→∞(x2+2)=∞\lim_{x \to \infty}\left(x^{2} + 2\right) = \infty
More at x→oo
lim⁡x→0−(x2+2)=2\lim_{x \to 0^-}\left(x^{2} + 2\right) = 2
More at x→0 from the left
lim⁡x→0+(x2+2)=2\lim_{x \to 0^+}\left(x^{2} + 2\right) = 2
More at x→0 from the right
lim⁡x→1−(x2+2)=3\lim_{x \to 1^-}\left(x^{2} + 2\right) = 3
More at x→1 from the left
lim⁡x→1+(x2+2)=3\lim_{x \to 1^+}\left(x^{2} + 2\right) = 3
More at x→1 from the right
lim⁡x→−∞(x2+2)=∞\lim_{x \to -\infty}\left(x^{2} + 2\right) = \infty
More at x→-oo
Rapid solution [src] 
6
66
Expand and simplify
Numerical answer [src] 
6.0
6.0
The graph
Limit of the function 2+x^2
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