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5/x
Limit of the function/ 5/x

Limit of the function 5/x

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You have entered [src] 
     /5\
 lim |-|
x->oo\x/
lim⁡x→∞(5x)\lim_{x \to \infty}\left(\frac{5}{x}\right) 
Limit(5/x, x, oo, dir='-')
Detail solution
Let's take the limit
lim⁡x→∞(5x)\lim_{x \to \infty}\left(\frac{5}{x}\right)
Let's divide numerator and denominator by x:
lim⁡x→∞(5x)\lim_{x \to \infty}\left(\frac{5}{x}\right) =
lim⁡x→∞(51x1)\lim_{x \to \infty}\left(\frac{5 \frac{1}{x}}{1}\right)
Do Replacement
u=1xu = \frac{1}{x}
then
lim⁡x→∞(51x1)=lim⁡u→0+(5u)\lim_{x \to \infty}\left(\frac{5 \frac{1}{x}}{1}\right) = \lim_{u \to 0^+}\left(5 u\right)
=
0⋅5=00 \cdot 5 = 0

The final answer:
lim⁡x→∞(5x)=0\lim_{x \to \infty}\left(\frac{5}{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
02468-8-6-4-2-1010-100100
Plot the graph
Rapid solution [src] 
0
00
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→∞(5x)=0\lim_{x \to \infty}\left(\frac{5}{x}\right) = 0
lim⁡x→0−(5x)=−∞\lim_{x \to 0^-}\left(\frac{5}{x}\right) = -\infty
More at x→0 from the left
lim⁡x→0+(5x)=∞\lim_{x \to 0^+}\left(\frac{5}{x}\right) = \infty
More at x→0 from the right
lim⁡x→1−(5x)=5\lim_{x \to 1^-}\left(\frac{5}{x}\right) = 5
More at x→1 from the left
lim⁡x→1+(5x)=5\lim_{x \to 1^+}\left(\frac{5}{x}\right) = 5
More at x→1 from the right
lim⁡x→−∞(5x)=0\lim_{x \to -\infty}\left(\frac{5}{x}\right) = 0
More at x→-oo
The graph
Limit of the function 5/x
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