Best solutions to - "Find the following limit. limn→∞2n2+25n3−3n−1"

Lipossig

Answered question

2020-11-10

Find the following limit.

lim_{n \to \infty} \frac{2 n^{2} + 2}{5 n^{3} - 3 n - 1}

Caren

Skilled2020-11-11Added 96 answers

Solution:

lim_{n \to \infty} \frac{2 n^{2} + 2}{5 n^{3} - 3 n - 1} = lim_{n \to \infty} \frac{n^{2} (2 + \frac{2}{n^{2}})}{n^{3} (5 - \frac{3}{n^{2}} - \frac{1}{n^{3}})}

= lim_{n \to \infty} \frac{(2 + \frac{2}{n^{2}})}{n (5 - \frac{3}{n^{2}} - \frac{1}{n^{3}})}

= lim_{n \to \infty} \frac{1}{n} \times lim_{n \to \infty} \frac{(2 + \frac{2}{n^{2}})}{(5 - \frac{3}{n^{2}} - \frac{1}{n^{3}})}

= lim_{n \to \infty} \frac{1}{n} \times \frac{(2 + 0)}{(5 - 0 - 0)}

= lim_{n \to \infty} \frac{1}{n} \times \frac{2}{5}

= 0 \times \frac{2}{5}

= 0

Jeffrey Jordon

Expert2022-04-01Added 2605 answers

Answer is given below (on video)

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