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x^2/3
Limit of the function/ x^2/3

Limit of the function x^2/3

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The solution

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     / 2\
     |x |
 lim |--|
x->1+\3 /
lim⁡x→1+(x23)\lim_{x \to 1^+}\left(\frac{x^{2}}{3}\right) 
Limit(x^2/3, 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
-2.0-1.5-1.0-0.52.00.00.51.01.502
Plot the graph
Rapid solution [src] 
1/3
13\frac{1}{3}
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→1−(x23)=13\lim_{x \to 1^-}\left(\frac{x^{2}}{3}\right) = \frac{1}{3}
More at x→1 from the left
lim⁡x→1+(x23)=13\lim_{x \to 1^+}\left(\frac{x^{2}}{3}\right) = \frac{1}{3}
lim⁡x→∞(x23)=∞\lim_{x \to \infty}\left(\frac{x^{2}}{3}\right) = \infty
More at x→oo
lim⁡x→0−(x23)=0\lim_{x \to 0^-}\left(\frac{x^{2}}{3}\right) = 0
More at x→0 from the left
lim⁡x→0+(x23)=0\lim_{x \to 0^+}\left(\frac{x^{2}}{3}\right) = 0
More at x→0 from the right
lim⁡x→−∞(x23)=∞\lim_{x \to -\infty}\left(\frac{x^{2}}{3}\right) = \infty
More at x→-oo
One‐sided limits [src] 
     / 2\
     |x |
 lim |--|
x->1+\3 /
lim⁡x→1+(x23)\lim_{x \to 1^+}\left(\frac{x^{2}}{3}\right) 
1/3
13\frac{1}{3} 
= 0.333333333333333
     / 2\
     |x |
 lim |--|
x->1-\3 /
lim⁡x→1−(x23)\lim_{x \to 1^-}\left(\frac{x^{2}}{3}\right) 
1/3
13\frac{1}{3} 
= 0.333333333333333
= 0.333333333333333
Numerical answer [src] 
0.333333333333333
0.333333333333333
The graph
Limit of the function x^2/3
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