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Proposition: Limit of a Rational Function

For any polynomials $p$, $q$ and a real number $a\in\mathbb R$ with $q(a)\neq 0,$ it follows for the rational function $\frac{p(x)}{q(x)}$ that $$\lim_{x\to a}\frac{p(x)}{q(x)}=\frac{p(a)}{q(a)}.$$

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References

Bibliography

  1. Kane, Jonathan: "Writing Proofs in Analysis", Springer, 2016