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Limit of the function/ sin(x/y)

Limit of the function sin(x/y)

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You have entered [src] 
        /x\
 lim sin|-|
y->oo   \y/
lim⁡y→∞sin⁡(xy)\lim_{y \to \infty} \sin{\left(\frac{x}{y} \right)} 
Limit(sin(x/y), y, 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
Rapid solution [src] 
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Expand and simplify
Other limits y→0, -oo, +oo, 1
lim⁡y→∞sin⁡(xy)=0\lim_{y \to \infty} \sin{\left(\frac{x}{y} \right)} = 0
lim⁡y→0−sin⁡(xy)=∞~xcos⁡(∞~x)\lim_{y \to 0^-} \sin{\left(\frac{x}{y} \right)} = \tilde{\infty} x \cos{\left(\tilde{\infty} x \right)}
More at y→0 from the left
lim⁡y→0+sin⁡(xy)=sin⁡(∞~x)\lim_{y \to 0^+} \sin{\left(\frac{x}{y} \right)} = \sin{\left(\tilde{\infty} x \right)}
More at y→0 from the right
lim⁡y→1−sin⁡(xy)=sin⁡(x)\lim_{y \to 1^-} \sin{\left(\frac{x}{y} \right)} = \sin{\left(x \right)}
More at y→1 from the left
lim⁡y→1+sin⁡(xy)=sin⁡(x)\lim_{y \to 1^+} \sin{\left(\frac{x}{y} \right)} = \sin{\left(x \right)}
More at y→1 from the right
lim⁡y→−∞sin⁡(xy)=0\lim_{y \to -\infty} \sin{\left(\frac{x}{y} \right)} = 0
More at y→-oo
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