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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

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     /  x  \
 lim |-----|
x->5+\2 + x/
$$\lim_{x \to 5^+}\left(\frac{x}{x + 2}\right)$$ 
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
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Rapid solution [src] 
5/7
$$\frac{5}{7}$$
Expand and simplify
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 5^-}\left(\frac{x}{x + 2}\right) = \frac{5}{7}$$
More at x→5 from the left
$$\lim_{x \to 5^+}\left(\frac{x}{x + 2}\right) = \frac{5}{7}$$
$$\lim_{x \to \infty}\left(\frac{x}{x + 2}\right) = 1$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{x}{x + 2}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x}{x + 2}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{x}{x + 2}\right) = \frac{1}{3}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x}{x + 2}\right) = \frac{1}{3}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x}{x + 2}\right) = 1$$
More at x→-oo
One‐sided limits [src] 
     /  x  \
 lim |-----|
x->5+\2 + x/
$$\lim_{x \to 5^+}\left(\frac{x}{x + 2}\right)$$ 
5/7
$$\frac{5}{7}$$ 
= 0.714285714285714
     /  x  \
 lim |-----|
x->5-\2 + x/
$$\lim_{x \to 5^-}\left(\frac{x}{x + 2}\right)$$ 
5/7
$$\frac{5}{7}$$ 
= 0.714285714285714
= 0.714285714285714
Numerical answer [src] 
0.714285714285714
0.714285714285714
The graph
Limit of the function x/(2+x)
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