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

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

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        /    /  1\ 
 lim x /  sin|1*-| 
x->oo\/      \  x/
lim⁡x→∞sin⁡1⋅1x(1⋅1x)\lim_{x \to \infty} \sin^{1 \cdot \frac{1}{x}}{\left(1 \cdot \frac{1}{x} \right)} 
Limit(sin(1/x)^(1/x), x, oo, dir='-')
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
02468-8-6-4-2-101002500
Plot the graph
Rapid solution [src] 
1
11
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→∞sin⁡1⋅1x(1⋅1x)=1\lim_{x \to \infty} \sin^{1 \cdot \frac{1}{x}}{\left(1 \cdot \frac{1}{x} \right)} = 1
lim⁡x→0−sin⁡1⋅1x(1⋅1x)\lim_{x \to 0^-} \sin^{1 \cdot \frac{1}{x}}{\left(1 \cdot \frac{1}{x} \right)}
More at x→0 from the left
lim⁡x→0+sin⁡1⋅1x(1⋅1x)\lim_{x \to 0^+} \sin^{1 \cdot \frac{1}{x}}{\left(1 \cdot \frac{1}{x} \right)}
More at x→0 from the right
lim⁡x→1−sin⁡1⋅1x(1⋅1x)=sin⁡(1)\lim_{x \to 1^-} \sin^{1 \cdot \frac{1}{x}}{\left(1 \cdot \frac{1}{x} \right)} = \sin{\left(1 \right)}
More at x→1 from the left
lim⁡x→1+sin⁡1⋅1x(1⋅1x)=sin⁡(1)\lim_{x \to 1^+} \sin^{1 \cdot \frac{1}{x}}{\left(1 \cdot \frac{1}{x} \right)} = \sin{\left(1 \right)}
More at x→1 from the right
lim⁡x→−∞sin⁡1⋅1x(1⋅1x)=1\lim_{x \to -\infty} \sin^{1 \cdot \frac{1}{x}}{\left(1 \cdot \frac{1}{x} \right)} = 1
More at x→-oo
The graph
Limit of the function sin(1/x)^(1/x)
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