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Limit of the function x*y^2

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      /   2\
 lim  \x*y /
x->-oo

\lim_{x \to -\infty}\left(x y^{2}\right)

Limit(x*y^2, x, -oo)

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]

        / 2\
-oo*sign\y /

- \infty \operatorname{sign}{\left(y^{2} \right)}

Expand and simplify

Other limits x→0, -oo, +oo, 1

\lim_{x \to -\infty}\left(x y^{2}\right) = - \infty \operatorname{sign}{\left(y^{2} \right)}

\lim_{x \to \infty}\left(x y^{2}\right) = \infty \operatorname{sign}{\left(y^{2} \right)}

\lim_{x \to 0^-}\left(x y^{2}\right) = 0

\lim_{x \to 0^+}\left(x y^{2}\right) = 0

\lim_{x \to 1^-}\left(x y^{2}\right) = y^{2}

\lim_{x \to 1^+}\left(x y^{2}\right) = y^{2}