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Limit of the function |x|/x

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You have entered [src] 
     /|x|\
 lim |---|
x->0+\ x /
lim⁡x→0+(∣x∣x)\lim_{x \to 0^+}\left(\frac{\left|{x}\right|}{x}\right) 
Limit(|x|/x, x, 0)
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02468-8-6-4-2-10102-2
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Rapid solution [src] 
1
11
Expand and simplify
One‐sided limits [src] 
     /|x|\
 lim |---|
x->0+\ x /
lim⁡x→0+(∣x∣x)\lim_{x \to 0^+}\left(\frac{\left|{x}\right|}{x}\right) 
1
11 
= 1.0
     /|x|\
 lim |---|
x->0-\ x /
lim⁡x→0−(∣x∣x)\lim_{x \to 0^-}\left(\frac{\left|{x}\right|}{x}\right) 
-1
−1-1 
= -1.0
= -1.0
Other limits x→0, -oo, +oo, 1
lim⁡x→0−(∣x∣x)=1\lim_{x \to 0^-}\left(\frac{\left|{x}\right|}{x}\right) = 1
More at x→0 from the left
lim⁡x→0+(∣x∣x)=1\lim_{x \to 0^+}\left(\frac{\left|{x}\right|}{x}\right) = 1
lim⁡x→∞(∣x∣x)=1\lim_{x \to \infty}\left(\frac{\left|{x}\right|}{x}\right) = 1
More at x→oo
lim⁡x→1−(∣x∣x)=1\lim_{x \to 1^-}\left(\frac{\left|{x}\right|}{x}\right) = 1
More at x→1 from the left
lim⁡x→1+(∣x∣x)=1\lim_{x \to 1^+}\left(\frac{\left|{x}\right|}{x}\right) = 1
More at x→1 from the right
lim⁡x→−∞(∣x∣x)=−1\lim_{x \to -\infty}\left(\frac{\left|{x}\right|}{x}\right) = -1
More at x→-oo
Numerical answer [src] 
1.0
1.0
The graph
Limit of the function |x|/x
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