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

Limit of the function cos(x)^cot(2*x)

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        cot(2*x)   
 lim cos        (x)
x->0+
lim⁡x→0+cos⁡cot⁡(2x)(x)\lim_{x \to 0^+} \cos^{\cot{\left(2 x \right)}}{\left(x \right)} 
Limit(cos(x)^cot(2*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
02468-8-6-4-2-101001e21
Plot the graph
Other limits x→0, -oo, +oo, 1
lim⁡x→0−cos⁡cot⁡(2x)(x)=1\lim_{x \to 0^-} \cos^{\cot{\left(2 x \right)}}{\left(x \right)} = 1
More at x→0 from the left
lim⁡x→0+cos⁡cot⁡(2x)(x)=1\lim_{x \to 0^+} \cos^{\cot{\left(2 x \right)}}{\left(x \right)} = 1
lim⁡x→∞cos⁡cot⁡(2x)(x)\lim_{x \to \infty} \cos^{\cot{\left(2 x \right)}}{\left(x \right)}
More at x→oo
lim⁡x→1−cos⁡cot⁡(2x)(x)=cos⁡1tan⁡(2)(1)\lim_{x \to 1^-} \cos^{\cot{\left(2 x \right)}}{\left(x \right)} = \cos^{\frac{1}{\tan{\left(2 \right)}}}{\left(1 \right)}
More at x→1 from the left
lim⁡x→1+cos⁡cot⁡(2x)(x)=cos⁡1tan⁡(2)(1)\lim_{x \to 1^+} \cos^{\cot{\left(2 x \right)}}{\left(x \right)} = \cos^{\frac{1}{\tan{\left(2 \right)}}}{\left(1 \right)}
More at x→1 from the right
lim⁡x→−∞cos⁡cot⁡(2x)(x)\lim_{x \to -\infty} \cos^{\cot{\left(2 x \right)}}{\left(x \right)}
More at x→-oo
One‐sided limits [src] 
        cot(2*x)   
 lim cos        (x)
x->0+
lim⁡x→0+cos⁡cot⁡(2x)(x)\lim_{x \to 0^+} \cos^{\cot{\left(2 x \right)}}{\left(x \right)} 
1
11 
= 1.0
        cot(2*x)   
 lim cos        (x)
x->0-
lim⁡x→0−cos⁡cot⁡(2x)(x)\lim_{x \to 0^-} \cos^{\cot{\left(2 x \right)}}{\left(x \right)} 
1
11 
= 1.0
= 1.0
Rapid solution [src] 
1
11
Expand and simplify
Numerical answer [src] 
1.0
1.0
The graph
Limit of the function cos(x)^cot(2*x)
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