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sign(sin(pi/x))
Limit of the function/ sign(sin(pi/x))

Limit of the function sign(sin(pi/x))

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         /   /pi\\
 lim sign|sin|--||
x->oo    \   \x //
$$\lim_{x \to \infty} \operatorname{sign}{\left(\sin{\left(\frac{\pi}{x} \right)} \right)}$$ 
Limit(sign(sin(pi/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
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Rapid solution [src] 
0
$$0$$
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Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \infty} \operatorname{sign}{\left(\sin{\left(\frac{\pi}{x} \right)} \right)} = 0$$
$$\lim_{x \to 0^-} \operatorname{sign}{\left(\sin{\left(\frac{\pi}{x} \right)} \right)} = \operatorname{sign}{\left(\left\langle -1, 1\right\rangle \right)}$$
More at x→0 from the left
$$\lim_{x \to 0^+} \operatorname{sign}{\left(\sin{\left(\frac{\pi}{x} \right)} \right)} = \operatorname{sign}{\left(\left\langle -1, 1\right\rangle \right)}$$
More at x→0 from the right
$$\lim_{x \to 1^-} \operatorname{sign}{\left(\sin{\left(\frac{\pi}{x} \right)} \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \operatorname{sign}{\left(\sin{\left(\frac{\pi}{x} \right)} \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \operatorname{sign}{\left(\sin{\left(\frac{\pi}{x} \right)} \right)} = 0$$
More at x→-oo
The graph
Limit of the function sign(sin(pi/x))
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