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(-1+sqrt(x))/(-3+x)
Limit of the function/ (-1+sqrt(x))/(-3+x)

Limit of the function (-1+sqrt(x))/(-3+x)

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     /       ___\
     |-1 + \/ x |
 lim |----------|
x->3+\  -3 + x  /
lim⁡x→3+(x−1x−3)\lim_{x \to 3^+}\left(\frac{\sqrt{x} - 1}{x - 3}\right) 
Limit((-1 + sqrt(x))/(-3 + x), x, 3)
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
6012345-6-5-4-3-2-1200-100
Plot the graph
Other limits x→0, -oo, +oo, 1
lim⁡x→3−(x−1x−3)=∞\lim_{x \to 3^-}\left(\frac{\sqrt{x} - 1}{x - 3}\right) = \infty
More at x→3 from the left
lim⁡x→3+(x−1x−3)=∞\lim_{x \to 3^+}\left(\frac{\sqrt{x} - 1}{x - 3}\right) = \infty
lim⁡x→∞(x−1x−3)=0\lim_{x \to \infty}\left(\frac{\sqrt{x} - 1}{x - 3}\right) = 0
More at x→oo
lim⁡x→0−(x−1x−3)=13\lim_{x \to 0^-}\left(\frac{\sqrt{x} - 1}{x - 3}\right) = \frac{1}{3}
More at x→0 from the left
lim⁡x→0+(x−1x−3)=13\lim_{x \to 0^+}\left(\frac{\sqrt{x} - 1}{x - 3}\right) = \frac{1}{3}
More at x→0 from the right
lim⁡x→1−(x−1x−3)=0\lim_{x \to 1^-}\left(\frac{\sqrt{x} - 1}{x - 3}\right) = 0
More at x→1 from the left
lim⁡x→1+(x−1x−3)=0\lim_{x \to 1^+}\left(\frac{\sqrt{x} - 1}{x - 3}\right) = 0
More at x→1 from the right
lim⁡x→−∞(x−1x−3)=0\lim_{x \to -\infty}\left(\frac{\sqrt{x} - 1}{x - 3}\right) = 0
More at x→-oo
Rapid solution [src] 
oo
∞\infty
Expand and simplify
One‐sided limits [src] 
     /       ___\
     |-1 + \/ x |
 lim |----------|
x->3+\  -3 + x  /
lim⁡x→3+(x−1x−3)\lim_{x \to 3^+}\left(\frac{\sqrt{x} - 1}{x - 3}\right) 
oo
∞\infty 
= 110.828187940107
     /       ___\
     |-1 + \/ x |
 lim |----------|
x->3-\  -3 + x  /
lim⁡x→3−(x−1x−3)\lim_{x \to 3^-}\left(\frac{\sqrt{x} - 1}{x - 3}\right) 
-oo
−∞-\infty 
= -110.250837319232
= -110.250837319232
Numerical answer [src] 
110.828187940107
110.828187940107
The graph
Limit of the function (-1+sqrt(x))/(-3+x)
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