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5*x^4
Limit of the function/ 5*x^4

Limit of the function 5*x^4

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     /   4\
 lim \5*x /
x->oo
lim⁡x→∞(5x4)\lim_{x \to \infty}\left(5 x^{4}\right) 
Limit(5*x^4, x, oo, dir='-')
Detail solution
Let's take the limit
lim⁡x→∞(5x4)\lim_{x \to \infty}\left(5 x^{4}\right)
Let's divide numerator and denominator by x^4:
lim⁡x→∞(5x4)\lim_{x \to \infty}\left(5 x^{4}\right) =
lim⁡x→∞1151x4\lim_{x \to \infty} \frac{1}{\frac{1}{5} \frac{1}{x^{4}}}
Do Replacement
u=1xu = \frac{1}{x}
then
lim⁡x→∞1151x4=lim⁡u→0+(5u4)\lim_{x \to \infty} \frac{1}{\frac{1}{5} \frac{1}{x^{4}}} = \lim_{u \to 0^+}\left(\frac{5}{u^{4}}\right)
=
50=∞\frac{5}{0} = \infty

The final answer:
lim⁡x→∞(5x4)=∞\lim_{x \to \infty}\left(5 x^{4}\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
02468-8-6-4-2-10100100000
Plot the graph
Rapid solution [src] 
oo
∞\infty
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→∞(5x4)=∞\lim_{x \to \infty}\left(5 x^{4}\right) = \infty
lim⁡x→0−(5x4)=0\lim_{x \to 0^-}\left(5 x^{4}\right) = 0
More at x→0 from the left
lim⁡x→0+(5x4)=0\lim_{x \to 0^+}\left(5 x^{4}\right) = 0
More at x→0 from the right
lim⁡x→1−(5x4)=5\lim_{x \to 1^-}\left(5 x^{4}\right) = 5
More at x→1 from the left
lim⁡x→1+(5x4)=5\lim_{x \to 1^+}\left(5 x^{4}\right) = 5
More at x→1 from the right
lim⁡x→−∞(5x4)=∞\lim_{x \to -\infty}\left(5 x^{4}\right) = \infty
More at x→-oo
The graph
Limit of the function 5*x^4
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