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2/(-3+x)
Limit of the function/ 2/(-3+x)

Limit of the function 2/(-3+x)

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The solution

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     /  2   \
 lim |------|
x->3+\-3 + x/
lim⁡x→3+(2x−3)\lim_{x \to 3^+}\left(\frac{2}{x - 3}\right) 
Limit(2/(-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
6012345-6-5-4-3-2-1-500500
Plot the graph
Other limits x→0, -oo, +oo, 1
lim⁡x→3−(2x−3)=∞\lim_{x \to 3^-}\left(\frac{2}{x - 3}\right) = \infty
More at x→3 from the left
lim⁡x→3+(2x−3)=∞\lim_{x \to 3^+}\left(\frac{2}{x - 3}\right) = \infty
lim⁡x→∞(2x−3)=0\lim_{x \to \infty}\left(\frac{2}{x - 3}\right) = 0
More at x→oo
lim⁡x→0−(2x−3)=−23\lim_{x \to 0^-}\left(\frac{2}{x - 3}\right) = - \frac{2}{3}
More at x→0 from the left
lim⁡x→0+(2x−3)=−23\lim_{x \to 0^+}\left(\frac{2}{x - 3}\right) = - \frac{2}{3}
More at x→0 from the right
lim⁡x→1−(2x−3)=−1\lim_{x \to 1^-}\left(\frac{2}{x - 3}\right) = -1
More at x→1 from the left
lim⁡x→1+(2x−3)=−1\lim_{x \to 1^+}\left(\frac{2}{x - 3}\right) = -1
More at x→1 from the right
lim⁡x→−∞(2x−3)=0\lim_{x \to -\infty}\left(\frac{2}{x - 3}\right) = 0
More at x→-oo
Rapid solution [src] 
oo
∞\infty
Expand and simplify
One‐sided limits [src] 
     /  2   \
 lim |------|
x->3+\-3 + x/
lim⁡x→3+(2x−3)\lim_{x \to 3^+}\left(\frac{2}{x - 3}\right) 
oo
∞\infty 
= 302.0
     /  2   \
 lim |------|
x->3-\-3 + x/
lim⁡x→3−(2x−3)\lim_{x \to 3^-}\left(\frac{2}{x - 3}\right) 
-oo
−∞-\infty 
= -302.0
= -302.0
Numerical answer [src] 
302.0
302.0
The graph
Limit of the function 2/(-3+x)
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