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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→∞((−1)x2)\lim_{x \to \infty}\left(\frac{\left(-1\right) x}{2}\right) 
Limit((-x)/2, x, oo, dir='-')
Detail solution
Let's take the limit
lim⁡x→∞((−1)x2)\lim_{x \to \infty}\left(\frac{\left(-1\right) x}{2}\right)
Let's divide numerator and denominator by x:
lim⁡x→∞((−1)x2)\lim_{x \to \infty}\left(\frac{\left(-1\right) x}{2}\right) =
lim⁡x→∞1(−1)21x\lim_{x \to \infty} \frac{1}{\left(-1\right) 2 \frac{1}{x}}
Do Replacement
u=1xu = \frac{1}{x}
then
lim⁡x→∞1(−1)21x=lim⁡u→0+(−12u)\lim_{x \to \infty} \frac{1}{\left(-1\right) 2 \frac{1}{x}} = \lim_{u \to 0^+}\left(- \frac{1}{2 u}\right)
=
−10⋅2=−∞- \frac{1}{0 \cdot 2} = -\infty

The final answer:
lim⁡x→∞((−1)x2)=−∞\lim_{x \to \infty}\left(\frac{\left(-1\right) 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
02468-8-6-4-2-1010-1010
Plot the graph
Rapid solution [src] 
-oo
−∞-\infty
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→∞((−1)x2)=−∞\lim_{x \to \infty}\left(\frac{\left(-1\right) x}{2}\right) = -\infty
lim⁡x→0−((−1)x2)=0\lim_{x \to 0^-}\left(\frac{\left(-1\right) x}{2}\right) = 0
More at x→0 from the left
lim⁡x→0+((−1)x2)=0\lim_{x \to 0^+}\left(\frac{\left(-1\right) x}{2}\right) = 0
More at x→0 from the right
lim⁡x→1−((−1)x2)=−12\lim_{x \to 1^-}\left(\frac{\left(-1\right) x}{2}\right) = - \frac{1}{2}
More at x→1 from the left
lim⁡x→1+((−1)x2)=−12\lim_{x \to 1^+}\left(\frac{\left(-1\right) x}{2}\right) = - \frac{1}{2}
More at x→1 from the right
lim⁡x→−∞((−1)x2)=∞\lim_{x \to -\infty}\left(\frac{\left(-1\right) x}{2}\right) = \infty
More at x→-oo
The graph
Limit of the function -x/2
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