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Limit of the function/ cot(pi*x)

Limit of the function cot(pi*x)

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You have entered [src] 
 lim cot(pi*x)
x->1+
lim⁡x→1+cot⁡(πx)\lim_{x \to 1^+} \cot{\left(\pi x \right)} 
Limit(cot(pi*x), 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
Rapid solution [src] 
oo
∞\infty
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→1−cot⁡(πx)=∞\lim_{x \to 1^-} \cot{\left(\pi x \right)} = \infty
More at x→1 from the left
lim⁡x→1+cot⁡(πx)=∞\lim_{x \to 1^+} \cot{\left(\pi x \right)} = \infty
lim⁡x→∞cot⁡(πx)=cot⁡(∞)\lim_{x \to \infty} \cot{\left(\pi x \right)} = \cot{\left(\infty \right)}
More at x→oo
lim⁡x→0−cot⁡(πx)=−∞\lim_{x \to 0^-} \cot{\left(\pi x \right)} = -\infty
More at x→0 from the left
lim⁡x→0+cot⁡(πx)=∞\lim_{x \to 0^+} \cot{\left(\pi x \right)} = \infty
More at x→0 from the right
lim⁡x→−∞cot⁡(πx)=−cot⁡(∞)\lim_{x \to -\infty} \cot{\left(\pi x \right)} = - \cot{\left(\infty \right)}
More at x→-oo
One‐sided limits [src] 
 lim cot(pi*x)
x->1+
lim⁡x→1+cot⁡(πx)\lim_{x \to 1^+} \cot{\left(\pi x \right)} 
oo
∞\infty 
= 48.0578575304964
 lim cot(pi*x)
x->1-
lim⁡x→1−cot⁡(πx)\lim_{x \to 1^-} \cot{\left(\pi x \right)} 
-oo
−∞-\infty 
= -48.0578575304964
= -48.0578575304964
Numerical answer [src] 
48.0578575304964
48.0578575304964
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