Mister Exam

Other calculators:

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

Limit of the function cot(x/2)

at →
v

For end points:

The graph:

from to

Piecewise:

The solution

You have entered [src] 
        /x\
 lim cot|-|
x->0+   \2/
lim⁡x→0+cot⁡(x2)\lim_{x \to 0^+} \cot{\left(\frac{x}{2} \right)} 
Limit(cot(x/2), 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
02468-8-6-4-2-1010-500500
Plot the graph
Rapid solution [src] 
oo
∞\infty
Expand and simplify
One‐sided limits [src] 
        /x\
 lim cot|-|
x->0+   \2/
lim⁡x→0+cot⁡(x2)\lim_{x \to 0^+} \cot{\left(\frac{x}{2} \right)} 
oo
∞\infty 
= 301.998896246434
        /x\
 lim cot|-|
x->0-   \2/
lim⁡x→0−cot⁡(x2)\lim_{x \to 0^-} \cot{\left(\frac{x}{2} \right)} 
-oo
−∞-\infty 
= -301.998896246434
= -301.998896246434
Other limits x→0, -oo, +oo, 1
lim⁡x→0−cot⁡(x2)=∞\lim_{x \to 0^-} \cot{\left(\frac{x}{2} \right)} = \infty
More at x→0 from the left
lim⁡x→0+cot⁡(x2)=∞\lim_{x \to 0^+} \cot{\left(\frac{x}{2} \right)} = \infty
lim⁡x→∞cot⁡(x2)=cot⁡(∞)\lim_{x \to \infty} \cot{\left(\frac{x}{2} \right)} = \cot{\left(\infty \right)}
More at x→oo
lim⁡x→1−cot⁡(x2)=1tan⁡(12)\lim_{x \to 1^-} \cot{\left(\frac{x}{2} \right)} = \frac{1}{\tan{\left(\frac{1}{2} \right)}}
More at x→1 from the left
lim⁡x→1+cot⁡(x2)=1tan⁡(12)\lim_{x \to 1^+} \cot{\left(\frac{x}{2} \right)} = \frac{1}{\tan{\left(\frac{1}{2} \right)}}
More at x→1 from the right
lim⁡x→−∞cot⁡(x2)=−cot⁡(∞)\lim_{x \to -\infty} \cot{\left(\frac{x}{2} \right)} = - \cot{\left(\infty \right)}
More at x→-oo
Numerical answer [src] 
301.998896246434
301.998896246434
The graph
Limit of the function cot(x/2)
    © Mister Exam – Calculator