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4*x/(1+x)
Limit of the function/ 4*x/(1+x)

Limit of the function 4*x/(1+x)

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The solution

You have entered [src] 
     / 4*x \
 lim |-----|
x->0+\1 + x/
lim⁡x→0+(4xx+1)\lim_{x \to 0^+}\left(\frac{4 x}{x + 1}\right) 
Limit((4*x)/(1 + x), x, 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
One‐sided limits [src] 
     / 4*x \
 lim |-----|
x->0+\1 + x/
lim⁡x→0+(4xx+1)\lim_{x \to 0^+}\left(\frac{4 x}{x + 1}\right) 
0
00 
= 2.93727144208228e-28
     / 4*x \
 lim |-----|
x->0-\1 + x/
lim⁡x→0−(4xx+1)\lim_{x \to 0^-}\left(\frac{4 x}{x + 1}\right) 
0
00 
= -2.38544570312941e-29
= -2.38544570312941e-29
Rapid solution [src] 
0
00
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→0−(4xx+1)=0\lim_{x \to 0^-}\left(\frac{4 x}{x + 1}\right) = 0
More at x→0 from the left
lim⁡x→0+(4xx+1)=0\lim_{x \to 0^+}\left(\frac{4 x}{x + 1}\right) = 0
lim⁡x→∞(4xx+1)=4\lim_{x \to \infty}\left(\frac{4 x}{x + 1}\right) = 4
More at x→oo
lim⁡x→1−(4xx+1)=2\lim_{x \to 1^-}\left(\frac{4 x}{x + 1}\right) = 2
More at x→1 from the left
lim⁡x→1+(4xx+1)=2\lim_{x \to 1^+}\left(\frac{4 x}{x + 1}\right) = 2
More at x→1 from the right
lim⁡x→−∞(4xx+1)=4\lim_{x \to -\infty}\left(\frac{4 x}{x + 1}\right) = 4
More at x→-oo
Numerical answer [src] 
2.93727144208228e-28
2.93727144208228e-28
The graph
Limit of the function 4*x/(1+x)
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