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3*x/(2+x^2)
Limit of the function/ 3*x/(2+x^2)

Limit of the function 3*x/(2+x^2)

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      / 3*x  \
 lim  |------|
x->-1+|     2|
      \2 + x /
lim⁡x→−1+(3xx2+2)\lim_{x \to -1^+}\left(\frac{3 x}{x^{2} + 2}\right) 
Limit((3*x)/(2 + x^2), x, -1)
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
-2.0-1.5-1.0-0.52.00.00.51.01.52.5-2.5
Plot the graph
Rapid solution [src] 
-1
−1-1
Expand and simplify
One‐sided limits [src] 
      / 3*x  \
 lim  |------|
x->-1+|     2|
      \2 + x /
lim⁡x→−1+(3xx2+2)\lim_{x \to -1^+}\left(\frac{3 x}{x^{2} + 2}\right) 
-1
−1-1 
= -1.0
      / 3*x  \
 lim  |------|
x->-1-|     2|
      \2 + x /
lim⁡x→−1−(3xx2+2)\lim_{x \to -1^-}\left(\frac{3 x}{x^{2} + 2}\right) 
-1
−1-1 
= -1.0
= -1.0
Other limits x→0, -oo, +oo, 1
lim⁡x→−1−(3xx2+2)=−1\lim_{x \to -1^-}\left(\frac{3 x}{x^{2} + 2}\right) = -1
More at x→-1 from the left
lim⁡x→−1+(3xx2+2)=−1\lim_{x \to -1^+}\left(\frac{3 x}{x^{2} + 2}\right) = -1
lim⁡x→∞(3xx2+2)=0\lim_{x \to \infty}\left(\frac{3 x}{x^{2} + 2}\right) = 0
More at x→oo
lim⁡x→0−(3xx2+2)=0\lim_{x \to 0^-}\left(\frac{3 x}{x^{2} + 2}\right) = 0
More at x→0 from the left
lim⁡x→0+(3xx2+2)=0\lim_{x \to 0^+}\left(\frac{3 x}{x^{2} + 2}\right) = 0
More at x→0 from the right
lim⁡x→1−(3xx2+2)=1\lim_{x \to 1^-}\left(\frac{3 x}{x^{2} + 2}\right) = 1
More at x→1 from the left
lim⁡x→1+(3xx2+2)=1\lim_{x \to 1^+}\left(\frac{3 x}{x^{2} + 2}\right) = 1
More at x→1 from the right
lim⁡x→−∞(3xx2+2)=0\lim_{x \to -\infty}\left(\frac{3 x}{x^{2} + 2}\right) = 0
More at x→-oo
Numerical answer [src] 
-1.0
-1.0
The graph
Limit of the function 3*x/(2+x^2)
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