Mister Exam

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Limit of the function x^2*y^2

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     / 2  2\
 lim \x *y /
y->3+

\lim_{y \to 3^+}\left(x^{2} y^{2}\right)

Limit(x^2*y^2, y, 3)

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
9*x

9 x^{2}

Expand and simplify

One‐sided limits [src]

     / 2  2\
 lim \x *y /
y->3+

\lim_{y \to 3^+}\left(x^{2} y^{2}\right)

   2
9*x

9 x^{2}

     / 2  2\
 lim \x *y /
y->3-

\lim_{y \to 3^-}\left(x^{2} y^{2}\right)

   2
9*x

9 x^{2}

9*x^2

Other limits y→0, -oo, +oo, 1

\lim_{y \to 3^-}\left(x^{2} y^{2}\right) = 9 x^{2}

\lim_{y \to 3^+}\left(x^{2} y^{2}\right) = 9 x^{2}

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

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

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

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

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

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