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Limit of the function/ sin(n*x)/n^2

Limit of the function sin(n*x)/n^2

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You have entered [src] 
     /sin(n*x)\
 lim |--------|
n->oo|    2   |
     \   n    /
lim⁡n→∞(sin⁡(nx)n2)\lim_{n \to \infty}\left(\frac{\sin{\left(n x \right)}}{n^{2}}\right) 
Limit(sin(n*x)/n^2, n, oo, dir='-')
Rapid solution [src] 
zoo*x*cos(zoo*x)
∞~xcos⁡(∞~x)\tilde{\infty} x \cos{\left(\tilde{\infty} x \right)}
Expand and simplify
Other limits n→0, -oo, +oo, 1
lim⁡n→∞(sin⁡(nx)n2)=∞~xcos⁡(∞~x)\lim_{n \to \infty}\left(\frac{\sin{\left(n x \right)}}{n^{2}}\right) = \tilde{\infty} x \cos{\left(\tilde{\infty} x \right)}
lim⁡n→0−(sin⁡(nx)n2)=−∞sign⁡(x)\lim_{n \to 0^-}\left(\frac{\sin{\left(n x \right)}}{n^{2}}\right) = - \infty \operatorname{sign}{\left(x \right)}
More at n→0 from the left
lim⁡n→0+(sin⁡(nx)n2)=∞sign⁡(x)\lim_{n \to 0^+}\left(\frac{\sin{\left(n x \right)}}{n^{2}}\right) = \infty \operatorname{sign}{\left(x \right)}
More at n→0 from the right
lim⁡n→1−(sin⁡(nx)n2)=sin⁡(x)\lim_{n \to 1^-}\left(\frac{\sin{\left(n x \right)}}{n^{2}}\right) = \sin{\left(x \right)}
More at n→1 from the left
lim⁡n→1+(sin⁡(nx)n2)=sin⁡(x)\lim_{n \to 1^+}\left(\frac{\sin{\left(n x \right)}}{n^{2}}\right) = \sin{\left(x \right)}
More at n→1 from the right
lim⁡n→−∞(sin⁡(nx)n2)=∞~xcos⁡(∞~x)\lim_{n \to -\infty}\left(\frac{\sin{\left(n x \right)}}{n^{2}}\right) = \tilde{\infty} x \cos{\left(\tilde{\infty} x \right)}
More at n→-oo
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