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3*x

Limit of the function 3*x

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The solution

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 lim  (3*x)
x->-oo     
limx(3x)\lim_{x \to -\infty}\left(3 x\right)
Limit(3*x, x, -oo)
Detail solution
Let's take the limit
limx(3x)\lim_{x \to -\infty}\left(3 x\right)
Let's divide numerator and denominator by x:
limx(3x)\lim_{x \to -\infty}\left(3 x\right) =
limx1131x\lim_{x \to -\infty} \frac{1}{\frac{1}{3} \frac{1}{x}}
Do Replacement
u=1xu = \frac{1}{x}
then
limx1131x=limu0+(3u)\lim_{x \to -\infty} \frac{1}{\frac{1}{3} \frac{1}{x}} = \lim_{u \to 0^+}\left(\frac{3}{u}\right)
=
30=\frac{3}{0} = -\infty

The final answer:
limx(3x)=\lim_{x \to -\infty}\left(3 x\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
02468-8-6-4-2-1010-5050
Rapid solution [src]
-oo
-\infty
Other limits x→0, -oo, +oo, 1
limx(3x)=\lim_{x \to -\infty}\left(3 x\right) = -\infty
limx(3x)=\lim_{x \to \infty}\left(3 x\right) = \infty
More at x→oo
limx0(3x)=0\lim_{x \to 0^-}\left(3 x\right) = 0
More at x→0 from the left
limx0+(3x)=0\lim_{x \to 0^+}\left(3 x\right) = 0
More at x→0 from the right
limx1(3x)=3\lim_{x \to 1^-}\left(3 x\right) = 3
More at x→1 from the left
limx1+(3x)=3\lim_{x \to 1^+}\left(3 x\right) = 3
More at x→1 from the right
The graph
Limit of the function 3*x