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Limit of the function/ y/x

Limit of the function y/x

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     /y\
 lim |-|
x->0+\x/
lim⁡x→0+(yx)\lim_{x \to 0^+}\left(\frac{y}{x}\right) 
Limit(y/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
Other limits x→0, -oo, +oo, 1
lim⁡x→0−(yx)=∞sign⁡(y)\lim_{x \to 0^-}\left(\frac{y}{x}\right) = \infty \operatorname{sign}{\left(y \right)}
More at x→0 from the left
lim⁡x→0+(yx)=∞sign⁡(y)\lim_{x \to 0^+}\left(\frac{y}{x}\right) = \infty \operatorname{sign}{\left(y \right)}
lim⁡x→∞(yx)=0\lim_{x \to \infty}\left(\frac{y}{x}\right) = 0
More at x→oo
lim⁡x→1−(yx)=y\lim_{x \to 1^-}\left(\frac{y}{x}\right) = y
More at x→1 from the left
lim⁡x→1+(yx)=y\lim_{x \to 1^+}\left(\frac{y}{x}\right) = y
More at x→1 from the right
lim⁡x→−∞(yx)=0\lim_{x \to -\infty}\left(\frac{y}{x}\right) = 0
More at x→-oo
Rapid solution [src] 
oo*sign(y)
∞sign⁡(y)\infty \operatorname{sign}{\left(y \right)}
Expand and simplify
One‐sided limits [src] 
     /y\
 lim |-|
x->0+\x/
lim⁡x→0+(yx)\lim_{x \to 0^+}\left(\frac{y}{x}\right) 
oo*sign(y)
∞sign⁡(y)\infty \operatorname{sign}{\left(y \right)} 
     /y\
 lim |-|
x->0-\x/
lim⁡x→0−(yx)\lim_{x \to 0^-}\left(\frac{y}{x}\right) 
-oo*sign(y)
−∞sign⁡(y)- \infty \operatorname{sign}{\left(y \right)} 
-oo*sign(y)
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