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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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           /x\
  lim   cot|-|
x->3*pi+   \3/
$$\lim_{x \to 3 \pi^+} \cot{\left(\frac{x}{3} \right)}$$ 
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
Plot the graph
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 3 \pi^-} \cot{\left(\frac{x}{3} \right)} = \infty$$
More at x→3*pi from the left
$$\lim_{x \to 3 \pi^+} \cot{\left(\frac{x}{3} \right)} = \infty$$
$$\lim_{x \to \infty} \cot{\left(\frac{x}{3} \right)} = \cot{\left(\infty \right)}$$
More at x→oo
$$\lim_{x \to 0^-} \cot{\left(\frac{x}{3} \right)} = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+} \cot{\left(\frac{x}{3} \right)} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \cot{\left(\frac{x}{3} \right)} = \frac{1}{\tan{\left(\frac{1}{3} \right)}}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \cot{\left(\frac{x}{3} \right)} = \frac{1}{\tan{\left(\frac{1}{3} \right)}}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \cot{\left(\frac{x}{3} \right)} = - \cot{\left(\infty \right)}$$
More at x→-oo
Rapid solution [src] 
oo
$$\infty$$
Expand and simplify
One‐sided limits [src] 
           /x\
  lim   cot|-|
x->3*pi+   \3/
$$\lim_{x \to 3 \pi^+} \cot{\left(\frac{x}{3} \right)}$$ 
oo
$$\infty$$ 
= 452.999264164613
           /x\
  lim   cot|-|
x->3*pi-   \3/
$$\lim_{x \to 3 \pi^-} \cot{\left(\frac{x}{3} \right)}$$ 
-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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