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Limit of the function/ x/2

Limit of the function x/2

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     /x\
 lim |-|
x->oo\2/
$$\lim_{x \to \infty}\left(\frac{x}{2}\right)$$ 
Limit(x/2, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(\frac{x}{2}\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty}\left(\frac{x}{2}\right)$$ =
$$\lim_{x \to \infty} \frac{1}{2 \cdot \frac{1}{x}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{2 \cdot \frac{1}{x}} = \lim_{u \to 0^+}\left(\frac{1}{2 u}\right)$$
=
$$\frac{1}{0 \cdot 2} = \infty$$

The final answer:
$$\lim_{x \to \infty}\left(\frac{x}{2}\right) = \infty$$
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
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \infty}\left(\frac{x}{2}\right) = \infty$$
$$\lim_{x \to 0^-}\left(\frac{x}{2}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x}{2}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{x}{2}\right) = \frac{1}{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x}{2}\right) = \frac{1}{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x}{2}\right) = -\infty$$
More at x→-oo
The graph
Limit of the function x/2
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