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3*x^5
Limit of the function/ 3*x^5

Limit of the function 3*x^5

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     /   5\
 lim \3*x /
x->oo
lim⁡x→∞(3x5)\lim_{x \to \infty}\left(3 x^{5}\right) 
Limit(3*x^5, x, oo, dir='-')
Detail solution
Let's take the limit
lim⁡x→∞(3x5)\lim_{x \to \infty}\left(3 x^{5}\right)
Let's divide numerator and denominator by x^5:
lim⁡x→∞(3x5)\lim_{x \to \infty}\left(3 x^{5}\right) =
lim⁡x→∞1131x5\lim_{x \to \infty} \frac{1}{\frac{1}{3} \frac{1}{x^{5}}}
Do Replacement
u=1xu = \frac{1}{x}
then
lim⁡x→∞1131x5=lim⁡u→0+(3u5)\lim_{x \to \infty} \frac{1}{\frac{1}{3} \frac{1}{x^{5}}} = \lim_{u \to 0^+}\left(\frac{3}{u^{5}}\right)
=
30=∞\frac{3}{0} = \infty

The final answer:
lim⁡x→∞(3x5)=∞\lim_{x \to \infty}\left(3 x^{5}\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
02468-8-6-4-2-1010-500000500000
Plot the graph
Rapid solution [src] 
oo
∞\infty
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→∞(3x5)=∞\lim_{x \to \infty}\left(3 x^{5}\right) = \infty
lim⁡x→0−(3x5)=0\lim_{x \to 0^-}\left(3 x^{5}\right) = 0
More at x→0 from the left
lim⁡x→0+(3x5)=0\lim_{x \to 0^+}\left(3 x^{5}\right) = 0
More at x→0 from the right
lim⁡x→1−(3x5)=3\lim_{x \to 1^-}\left(3 x^{5}\right) = 3
More at x→1 from the left
lim⁡x→1+(3x5)=3\lim_{x \to 1^+}\left(3 x^{5}\right) = 3
More at x→1 from the right
lim⁡x→−∞(3x5)=−∞\lim_{x \to -\infty}\left(3 x^{5}\right) = -\infty
More at x→-oo
The graph
Limit of the function 3*x^5
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