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

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

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The solution

You have entered [src] 
                   1   
                 ------
                 sin(x)
 lim (1 - sin(x))      
x->0+
lim⁡x→0+(1−sin⁡(x))1sin⁡(x)\lim_{x \to 0^+} \left(1 - \sin{\left(x \right)}\right)^{\frac{1}{\sin{\left(x \right)}}} 
Limit((1 - sin(x))^(1/sin(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
02468-8-6-4-2-10100.01.0
Plot the graph
One‐sided limits [src] 
                   1   
                 ------
                 sin(x)
 lim (1 - sin(x))      
x->0+
lim⁡x→0+(1−sin⁡(x))1sin⁡(x)\lim_{x \to 0^+} \left(1 - \sin{\left(x \right)}\right)^{\frac{1}{\sin{\left(x \right)}}} 
 -1
e
e−1e^{-1} 
= 0.367879441171442
                   1   
                 ------
                 sin(x)
 lim (1 - sin(x))      
x->0-
lim⁡x→0−(1−sin⁡(x))1sin⁡(x)\lim_{x \to 0^-} \left(1 - \sin{\left(x \right)}\right)^{\frac{1}{\sin{\left(x \right)}}} 
 -1
e
e−1e^{-1} 
= 0.367879441171442
= 0.367879441171442
Rapid solution [src] 
 -1
e
e−1e^{-1}
Expand and simplify
Numerical answer [src] 
0.367879441171442
0.367879441171442
The graph
Limit of the function (1-sin(x))^(1/sin(x))
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