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4*x

Limit of the function 4*x

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The solution

You have entered [src]
 lim (4*x)
x->oo     
limx(4x)\lim_{x \to \infty}\left(4 x\right)
Limit(4*x, x, oo, dir='-')
Detail solution
Let's take the limit
limx(4x)\lim_{x \to \infty}\left(4 x\right)
Let's divide numerator and denominator by x:
limx(4x)\lim_{x \to \infty}\left(4 x\right) =
limx1141x\lim_{x \to \infty} \frac{1}{\frac{1}{4} \frac{1}{x}}
Do Replacement
u=1xu = \frac{1}{x}
then
limx1141x=limu0+(4u)\lim_{x \to \infty} \frac{1}{\frac{1}{4} \frac{1}{x}} = \lim_{u \to 0^+}\left(\frac{4}{u}\right)
=
40=\frac{4}{0} = \infty

The final answer:
limx(4x)=\lim_{x \to \infty}\left(4 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
02468-8-6-4-2-1010-100100
Other limits x→0, -oo, +oo, 1
limx(4x)=\lim_{x \to \infty}\left(4 x\right) = \infty
limx0(4x)=0\lim_{x \to 0^-}\left(4 x\right) = 0
More at x→0 from the left
limx0+(4x)=0\lim_{x \to 0^+}\left(4 x\right) = 0
More at x→0 from the right
limx1(4x)=4\lim_{x \to 1^-}\left(4 x\right) = 4
More at x→1 from the left
limx1+(4x)=4\lim_{x \to 1^+}\left(4 x\right) = 4
More at x→1 from the right
limx(4x)=\lim_{x \to -\infty}\left(4 x\right) = -\infty
More at x→-oo
Rapid solution [src]
oo
\infty
The graph
Limit of the function 4*x