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2.2: Teoremas de Límite
https://espanol.libretexts.org/Matematicas/Analisis/Introducci%C3%B3n_al_An%C3%A1lisis_Matem%C3%A1tico_I_(Lafferriere%2C_Lafferriere_y_Nguyen)/02%3A_Secuencias/2.02%3A_Teoremas_de_L%C3%ADmite
$\left|a_{n} b_{n}-a b\right|=\left|a_{n} b_{n}-a_{n} b+a_{n} b-a b\right| \leq\left|a_{n}\right|\left|b_{n}-b\right|+|b|\left|a_{n}-a\right|.$ \[\lim _{n \rightarrow \infty} a_{n}=\lim _{n \rightar... $\left|a_{n} b_{n}-a b\right|=\left|a_{n} b_{n}-a_{n} b+a_{n} b-a b\right| \leq\left|a_{n}\right|\left|b_{n}-b\right|+|b|\left|a_{n}-a\right|.$ $\lim _{n \rightarrow \infty} a_{n}=\lim _{n \rightarrow \infty} \frac{3-2 / n+5 / n^{2}}{1 / n^{2}-4 / n+7}=\frac{\lim _{n \rightarrow \infty} 3-\lim _{n \rightarrow \infty} 2 / n+\lim _{n \rightarrow \infty} 5 / n^{2}}{\lim _{n \rightarrow \infty} 1 / n^{2}-\lim _{n \rightarrow \infty} 4 / n+\lim _{n \rightarrow \infty} 7}=\frac{3}{7}.$

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