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

Limit of the function x/(2+x)

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The solution

You have entered [src] 
     /  x  \
 lim |-----|
x->5+\2 + x/
lim⁡x→5+(xx+2)\lim_{x \to 5^+}\left(\frac{x}{x + 2}\right) 
Limit(x/(2 + x), x, 5)
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
02468-8-6-4-2-1010-5050
Plot the graph
Rapid solution [src] 
5/7
57\frac{5}{7}
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→5−(xx+2)=57\lim_{x \to 5^-}\left(\frac{x}{x + 2}\right) = \frac{5}{7}
More at x→5 from the left
lim⁡x→5+(xx+2)=57\lim_{x \to 5^+}\left(\frac{x}{x + 2}\right) = \frac{5}{7}
lim⁡x→∞(xx+2)=1\lim_{x \to \infty}\left(\frac{x}{x + 2}\right) = 1
More at x→oo
lim⁡x→0−(xx+2)=0\lim_{x \to 0^-}\left(\frac{x}{x + 2}\right) = 0
More at x→0 from the left
lim⁡x→0+(xx+2)=0\lim_{x \to 0^+}\left(\frac{x}{x + 2}\right) = 0
More at x→0 from the right
lim⁡x→1−(xx+2)=13\lim_{x \to 1^-}\left(\frac{x}{x + 2}\right) = \frac{1}{3}
More at x→1 from the left
lim⁡x→1+(xx+2)=13\lim_{x \to 1^+}\left(\frac{x}{x + 2}\right) = \frac{1}{3}
More at x→1 from the right
lim⁡x→−∞(xx+2)=1\lim_{x \to -\infty}\left(\frac{x}{x + 2}\right) = 1
More at x→-oo
One‐sided limits [src] 
     /  x  \
 lim |-----|
x->5+\2 + x/
lim⁡x→5+(xx+2)\lim_{x \to 5^+}\left(\frac{x}{x + 2}\right) 
5/7
57\frac{5}{7} 
= 0.714285714285714
     /  x  \
 lim |-----|
x->5-\2 + x/
lim⁡x→5−(xx+2)\lim_{x \to 5^-}\left(\frac{x}{x + 2}\right) 
5/7
57\frac{5}{7} 
= 0.714285714285714
= 0.714285714285714
Numerical answer [src] 
0.714285714285714
0.714285714285714
The graph
Limit of the function x/(2+x)
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