lim (8n + 1)/(n ^ 2 – 2n + 1) lim ((n – 1) ^ 2 * (3n + 1))/(n ^ 3 + 3n – 1)

1 bình luận về “lim (8n + 1)/(n ^ 2 – 2n + 1) lim ((n – 1) ^ 2 * (3n + 1))/(n ^ 3 + 3n – 1)”

1. lim {8n + 1}/{n^2 – 2n + 1}$\\$

   = lim {n^2. (8/{n} + 1/{n^2})}/{n^2. (1 – 2/{n} + 1/{n^2})}$\\$

   = lim {8/{n} + 1/{n^2}}/{1 – 2/{n} + 1/{n^2}}$\\$

   = 0/1 = 0$\\$

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   lim {(n – 1)^2. (3n + 1)}/{n^3 + 3n – 1}$\\$

   = lim {(n^2 – 2n + 1). (3n + 1)}/{n^3 + 3n – 1}$\\$

   = lim {3n^3 – 5n^2 + n + 1}/{n^3 + 3n – 1}$\\$

   = lim {n^3. (3 – 5/{n} + 1/{n^2} + 1/{n^3})}/{n^3. (1 + 3/{n^2} – 1/{n^3})}$\\$

   = lim {3 – 5/{n} + 1/{n^2} + 1/{n^3}}/{1 + 3/{n^2} – 1/{n^3}}$\\$

   = 3 $\\$

    

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