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(cos(x)+sin(x))^(1/x)
Limit of the function/ (cos(x)+sin(x))^(1/x)

Limit of the function (cos(x)+sin(x))^(1/x)

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     x _________________
 lim \/ cos(x) + sin(x) 
x->0+
lim⁡x→0+(sin⁡(x)+cos⁡(x))1x\lim_{x \to 0^+} \left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{\frac{1}{x}} 
Limit((cos(x) + sin(x))^(1/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
02468-8-6-4-2-1010025
Plot the graph
One‐sided limits [src] 
     x _________________
 lim \/ cos(x) + sin(x) 
x->0+
lim⁡x→0+(sin⁡(x)+cos⁡(x))1x\lim_{x \to 0^+} \left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{\frac{1}{x}} 
E
ee 
= 2.71828182845905
     x _________________
 lim \/ cos(x) + sin(x) 
x->0-
lim⁡x→0−(sin⁡(x)+cos⁡(x))1x\lim_{x \to 0^-} \left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{\frac{1}{x}} 
E
ee 
= 2.71828182845905
= 2.71828182845905
Rapid solution [src] 
E
ee
Expand and simplify
Numerical answer [src] 
2.71828182845905
2.71828182845905
The graph
Limit of the function (cos(x)+sin(x))^(1/x)
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