Mister Exam

Other calculators:

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

Limit of the function cot(x)^cos(x)

at →
v

For end points:

The graph:

from to

Piecewise:

The solution

You have entered [src] 
         cos(x)   
 lim  cot      (x)
   pi             
x->--+            
   2
lim⁡x→π2+cot⁡cos⁡(x)(x)\lim_{x \to \frac{\pi}{2}^+} \cot^{\cos{\left(x \right)}}{\left(x \right)} 
Limit(cot(x)^cos(x), x, pi/2)
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
-3.0-2.5-2.0-1.5-1.0-0.50.00.51.01.52.02.53.0-5050
Plot the graph
Rapid solution [src] 
1
11
Expand and simplify
One‐sided limits [src] 
         cos(x)   
 lim  cot      (x)
   pi             
x->--+            
   2
lim⁡x→π2+cot⁡cos⁡(x)(x)\lim_{x \to \frac{\pi}{2}^+} \cot^{\cos{\left(x \right)}}{\left(x \right)} 
1
11 
= (1.00191868618493 - 0.000831463027735788j)
         cos(x)   
 lim  cot      (x)
   pi             
x->---            
   2
lim⁡x→π2−cot⁡cos⁡(x)(x)\lim_{x \to \frac{\pi}{2}^-} \cot^{\cos{\left(x \right)}}{\left(x \right)} 
1
11 
= 0.9978981007012
= 0.9978981007012
Other limits x→0, -oo, +oo, 1
lim⁡x→π2−cot⁡cos⁡(x)(x)=1\lim_{x \to \frac{\pi}{2}^-} \cot^{\cos{\left(x \right)}}{\left(x \right)} = 1
More at x→pi/2 from the left
lim⁡x→π2+cot⁡cos⁡(x)(x)=1\lim_{x \to \frac{\pi}{2}^+} \cot^{\cos{\left(x \right)}}{\left(x \right)} = 1
lim⁡x→∞cot⁡cos⁡(x)(x)\lim_{x \to \infty} \cot^{\cos{\left(x \right)}}{\left(x \right)}
More at x→oo
lim⁡x→0−cot⁡cos⁡(x)(x)=−∞\lim_{x \to 0^-} \cot^{\cos{\left(x \right)}}{\left(x \right)} = -\infty
More at x→0 from the left
lim⁡x→0+cot⁡cos⁡(x)(x)=∞\lim_{x \to 0^+} \cot^{\cos{\left(x \right)}}{\left(x \right)} = \infty
More at x→0 from the right
lim⁡x→1−cot⁡cos⁡(x)(x)=tan⁡−cos⁡(1)(1)\lim_{x \to 1^-} \cot^{\cos{\left(x \right)}}{\left(x \right)} = \tan^{- \cos{\left(1 \right)}}{\left(1 \right)}
More at x→1 from the left
lim⁡x→1+cot⁡cos⁡(x)(x)=tan⁡−cos⁡(1)(1)\lim_{x \to 1^+} \cot^{\cos{\left(x \right)}}{\left(x \right)} = \tan^{- \cos{\left(1 \right)}}{\left(1 \right)}
More at x→1 from the right
lim⁡x→−∞cot⁡cos⁡(x)(x)\lim_{x \to -\infty} \cot^{\cos{\left(x \right)}}{\left(x \right)}
More at x→-oo
Numerical answer [src] 
(1.00191868618493 - 0.000831463027735788j)
(1.00191868618493 - 0.000831463027735788j)
The graph
Limit of the function cot(x)^cos(x)
    © Mister Exam – Calculator