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cot(x/3)
Limit of the function/ cot(x/3)

Limit of the function cot(x/3)

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You have entered [src] 
           /x\
  lim   cot|-|
x->3*pi+   \3/
lim⁡x→3π+cot⁡(x3)\lim_{x \to 3 \pi^+} \cot{\left(\frac{x}{3} \right)} 
Limit(cot(x/3), x, 3*pi)
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
05-15-10-51015-50000000000000005000000000000000
Plot the graph
Other limits x→0, -oo, +oo, 1
lim⁡x→3π−cot⁡(x3)=∞\lim_{x \to 3 \pi^-} \cot{\left(\frac{x}{3} \right)} = \infty
More at x→3*pi from the left
lim⁡x→3π+cot⁡(x3)=∞\lim_{x \to 3 \pi^+} \cot{\left(\frac{x}{3} \right)} = \infty
lim⁡x→∞cot⁡(x3)=cot⁡(∞)\lim_{x \to \infty} \cot{\left(\frac{x}{3} \right)} = \cot{\left(\infty \right)}
More at x→oo
lim⁡x→0−cot⁡(x3)=−∞\lim_{x \to 0^-} \cot{\left(\frac{x}{3} \right)} = -\infty
More at x→0 from the left
lim⁡x→0+cot⁡(x3)=∞\lim_{x \to 0^+} \cot{\left(\frac{x}{3} \right)} = \infty
More at x→0 from the right
lim⁡x→1−cot⁡(x3)=1tan⁡(13)\lim_{x \to 1^-} \cot{\left(\frac{x}{3} \right)} = \frac{1}{\tan{\left(\frac{1}{3} \right)}}
More at x→1 from the left
lim⁡x→1+cot⁡(x3)=1tan⁡(13)\lim_{x \to 1^+} \cot{\left(\frac{x}{3} \right)} = \frac{1}{\tan{\left(\frac{1}{3} \right)}}
More at x→1 from the right
lim⁡x→−∞cot⁡(x3)=−cot⁡(∞)\lim_{x \to -\infty} \cot{\left(\frac{x}{3} \right)} = - \cot{\left(\infty \right)}
More at x→-oo
Rapid solution [src] 
oo
∞\infty
Expand and simplify
One‐sided limits [src] 
           /x\
  lim   cot|-|
x->3*pi+   \3/
lim⁡x→3π+cot⁡(x3)\lim_{x \to 3 \pi^+} \cot{\left(\frac{x}{3} \right)} 
oo
∞\infty 
= 452.999264164613
           /x\
  lim   cot|-|
x->3*pi-   \3/
lim⁡x→3π−cot⁡(x3)\lim_{x \to 3 \pi^-} \cot{\left(\frac{x}{3} \right)} 
-oo
−∞-\infty 
= -452.999264164563
= -452.999264164563
Numerical answer [src] 
452.999264164613
452.999264164613
The graph
Limit of the function cot(x/3)
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