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Limit of the function/ -2/x

Limit of the function -2/x

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     /-2 \
 lim |---|
x->oo\ x /
lim⁡x→∞(−2x)\lim_{x \to \infty}\left(- \frac{2}{x}\right) 
Limit(-2/x, x, oo, dir='-')
Detail solution
Let's take the limit
lim⁡x→∞(−2x)\lim_{x \to \infty}\left(- \frac{2}{x}\right)
Let's divide numerator and denominator by x:
lim⁡x→∞(−2x)\lim_{x \to \infty}\left(- \frac{2}{x}\right) =
lim⁡x→∞((−1)21x1)\lim_{x \to \infty}\left(\frac{\left(-1\right) 2 \frac{1}{x}}{1}\right)
Do Replacement
u=1xu = \frac{1}{x}
then
lim⁡x→∞((−1)21x1)=lim⁡u→0+(−2u)\lim_{x \to \infty}\left(\frac{\left(-1\right) 2 \frac{1}{x}}{1}\right) = \lim_{u \to 0^+}\left(- 2 u\right)
=
−0=0- 0 = 0

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