Mister Exam

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Limit of the function x^2/y^2

You have entered [src]

     / 2\
     |x |
 lim |--|
x->oo| 2|
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\lim_{x \to \infty}\left(\frac{x^{2}}{y^{2}}\right)

Limit(x^2/y^2, 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

Rapid solution [src]

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oo*sign|--|
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       \y /

\infty \operatorname{sign}{\left(\frac{1}{y^{2}} \right)}

Expand and simplify

Other limits x→0, -oo, +oo, 1

\lim_{x \to \infty}\left(\frac{x^{2}}{y^{2}}\right) = \infty \operatorname{sign}{\left(\frac{1}{y^{2}} \right)}

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

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

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

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

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