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(1-sin(x))^cot(x)
Limit of the function/ (1-sin(x))^cot(x)

Limit of the function (1-sin(x))^cot(x)

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                 cot(x)
 lim (1 - sin(x))      
x->0+
$$\lim_{x \to 0^+} \left(1 - \sin{\left(x \right)}\right)^{\cot{\left(x \right)}}$$ 
Limit((1 - sin(x))^cot(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
Plot the graph
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-} \left(1 - \sin{\left(x \right)}\right)^{\cot{\left(x \right)}} = e^{-1}$$
More at x→0 from the left
$$\lim_{x \to 0^+} \left(1 - \sin{\left(x \right)}\right)^{\cot{\left(x \right)}} = e^{-1}$$
$$\lim_{x \to \infty} \left(1 - \sin{\left(x \right)}\right)^{\cot{\left(x \right)}}$$
More at x→oo
$$\lim_{x \to 1^-} \left(1 - \sin{\left(x \right)}\right)^{\cot{\left(x \right)}} = \left(1 - \sin{\left(1 \right)}\right)^{\frac{1}{\tan{\left(1 \right)}}}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \left(1 - \sin{\left(x \right)}\right)^{\cot{\left(x \right)}} = \left(1 - \sin{\left(1 \right)}\right)^{\frac{1}{\tan{\left(1 \right)}}}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \left(1 - \sin{\left(x \right)}\right)^{\cot{\left(x \right)}}$$
More at x→-oo
Rapid solution [src] 
 -1
e
$$e^{-1}$$
Expand and simplify
One‐sided limits [src] 
                 cot(x)
 lim (1 - sin(x))      
x->0+
$$\lim_{x \to 0^+} \left(1 - \sin{\left(x \right)}\right)^{\cot{\left(x \right)}}$$ 
 -1
e
$$e^{-1}$$ 
= 0.367879441171442
                 cot(x)
 lim (1 - sin(x))      
x->0-
$$\lim_{x \to 0^-} \left(1 - \sin{\left(x \right)}\right)^{\cot{\left(x \right)}}$$ 
 -1
e
$$e^{-1}$$ 
= 0.367879441171442
= 0.367879441171442
Numerical answer [src] 
0.367879441171442
0.367879441171442
The graph
Limit of the function (1-sin(x))^cot(x)
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