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

Limit of the function cot(x)/x

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     /cot(x)\
 lim |------|
x->0+\  x   /
lim⁡x→0+(cot⁡(x)x)\lim_{x \to 0^+}\left(\frac{\cot{\left(x \right)}}{x}\right) 
Limit(cot(x)/x, x, 0)
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
02468-8-6-4-2-1010-2500025000
Plot the graph
Other limits x→0, -oo, +oo, 1
lim⁡x→0−(cot⁡(x)x)=∞\lim_{x \to 0^-}\left(\frac{\cot{\left(x \right)}}{x}\right) = \infty
More at x→0 from the left
lim⁡x→0+(cot⁡(x)x)=∞\lim_{x \to 0^+}\left(\frac{\cot{\left(x \right)}}{x}\right) = \infty
lim⁡x→∞(cot⁡(x)x)\lim_{x \to \infty}\left(\frac{\cot{\left(x \right)}}{x}\right)
More at x→oo
lim⁡x→1−(cot⁡(x)x)=1tan⁡(1)\lim_{x \to 1^-}\left(\frac{\cot{\left(x \right)}}{x}\right) = \frac{1}{\tan{\left(1 \right)}}
More at x→1 from the left
lim⁡x→1+(cot⁡(x)x)=1tan⁡(1)\lim_{x \to 1^+}\left(\frac{\cot{\left(x \right)}}{x}\right) = \frac{1}{\tan{\left(1 \right)}}
More at x→1 from the right
lim⁡x→−∞(cot⁡(x)x)\lim_{x \to -\infty}\left(\frac{\cot{\left(x \right)}}{x}\right)
More at x→-oo
One‐sided limits [src] 
     /cot(x)\
 lim |------|
x->0+\  x   /
lim⁡x→0+(cot⁡(x)x)\lim_{x \to 0^+}\left(\frac{\cot{\left(x \right)}}{x}\right) 
oo
∞\infty 
= 22800.666665692
     /cot(x)\
 lim |------|
x->0-\  x   /
lim⁡x→0−(cot⁡(x)x)\lim_{x \to 0^-}\left(\frac{\cot{\left(x \right)}}{x}\right) 
oo
∞\infty 
= 22800.666665692
= 22800.666665692
Rapid solution [src] 
oo
∞\infty
Expand and simplify
Numerical answer [src] 
22800.666665692
22800.666665692
The graph
Limit of the function cot(x)/x
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