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cot(2*x)
Limit of the function/ cot(2*x)

Limit of the function cot(2*x)

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You have entered [src] 
 lim  cot(2*x)
   pi         
x->--+        
   4
lim⁡x→π4+cot⁡(2x)\lim_{x \to \frac{\pi}{4}^+} \cot{\left(2 x \right)} 
Limit(cot(2*x), x, pi/4)
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
-1.50-1.25-1.00-0.75-0.50-0.250.000.250.500.751.001.251.50-1000000000000000010000000000000000
Plot the graph
Rapid solution [src] 
0
00
Expand and simplify
One‐sided limits [src] 
 lim  cot(2*x)
   pi         
x->--+        
   4
lim⁡x→π4+cot⁡(2x)\lim_{x \to \frac{\pi}{4}^+} \cot{\left(2 x \right)} 
0
00 
= 6.12323399569652e-17
 lim  cot(2*x)
   pi         
x->---        
   4
lim⁡x→π4−cot⁡(2x)\lim_{x \to \frac{\pi}{4}^-} \cot{\left(2 x \right)} 
0
00 
= 6.12323399577702e-17
= 6.12323399577702e-17
Other limits x→0, -oo, +oo, 1
lim⁡x→π4−cot⁡(2x)=0\lim_{x \to \frac{\pi}{4}^-} \cot{\left(2 x \right)} = 0
More at x→pi/4 from the left
lim⁡x→π4+cot⁡(2x)=0\lim_{x \to \frac{\pi}{4}^+} \cot{\left(2 x \right)} = 0
lim⁡x→∞cot⁡(2x)=cot⁡(∞)\lim_{x \to \infty} \cot{\left(2 x \right)} = \cot{\left(\infty \right)}
More at x→oo
lim⁡x→0−cot⁡(2x)=−∞\lim_{x \to 0^-} \cot{\left(2 x \right)} = -\infty
More at x→0 from the left
lim⁡x→0+cot⁡(2x)=∞\lim_{x \to 0^+} \cot{\left(2 x \right)} = \infty
More at x→0 from the right
lim⁡x→1−cot⁡(2x)=1tan⁡(2)\lim_{x \to 1^-} \cot{\left(2 x \right)} = \frac{1}{\tan{\left(2 \right)}}
More at x→1 from the left
lim⁡x→1+cot⁡(2x)=1tan⁡(2)\lim_{x \to 1^+} \cot{\left(2 x \right)} = \frac{1}{\tan{\left(2 \right)}}
More at x→1 from the right
lim⁡x→−∞cot⁡(2x)=−cot⁡(∞)\lim_{x \to -\infty} \cot{\left(2 x \right)} = - \cot{\left(\infty \right)}
More at x→-oo
Numerical answer [src] 
6.12323399569652e-17
6.12323399569652e-17
The graph
Limit of the function cot(2*x)
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