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4/(2+x)
Limit of the function/ 4/(2+x)

Limit of the function 4/(2+x)

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The solution

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      /  4  \
 lim  |-----|
x->-2+\2 + x/
$$\lim_{x \to -2^+}\left(\frac{4}{x + 2}\right)$$ 
Limit(4/(2 + x), 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
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Rapid solution [src] 
oo
$$\infty$$
Expand and simplify
One‐sided limits [src] 
      /  4  \
 lim  |-----|
x->-2+\2 + x/
$$\lim_{x \to -2^+}\left(\frac{4}{x + 2}\right)$$ 
oo
$$\infty$$ 
= 604.0
      /  4  \
 lim  |-----|
x->-2-\2 + x/
$$\lim_{x \to -2^-}\left(\frac{4}{x + 2}\right)$$ 
-oo
$$-\infty$$ 
= -604.0
= -604.0
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to -2^-}\left(\frac{4}{x + 2}\right) = \infty$$
More at x→-2 from the left
$$\lim_{x \to -2^+}\left(\frac{4}{x + 2}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{4}{x + 2}\right) = 0$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{4}{x + 2}\right) = 2$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{4}{x + 2}\right) = 2$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{4}{x + 2}\right) = \frac{4}{3}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{4}{x + 2}\right) = \frac{4}{3}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{4}{x + 2}\right) = 0$$
More at x→-oo
Numerical answer [src] 
604.0
604.0
The graph
Limit of the function 4/(2+x)
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