Question

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Answer 1

$1, l i m \frac{- 5 n + 3}{2 n - 6} = l i m \frac{n . (- 5 + \frac{3}{n})}{n (2 - \frac{6}{n})} = l i m \frac{- 5 + \frac{3}{n}}{2 - \frac{6}{n}} = - \frac{5}{2} 2, l i m \frac{2 n^{3} - 4 n^{2} + 3 n + 3}{n^{3} - 5 n + 7} = l i m \frac{n^{3} . (2 - \frac{4}{n} + \frac{3}{n^{2}} + \frac{3}{n^{3}})}{n^{3} . (1 - \frac{5}{n^{2}} + \frac{7}{n^{3}})} = l i m \frac{2 - \frac{4}{n} + \frac{3}{n^{2}} + \frac{3}{n^{3}}}{1 - \frac{5}{n^{2}} + \frac{7}{n^{3}}} = 2 3, l i m \frac{- 3 n + 2}{n^{3} + 2 n - 1} = l i m \frac{n . (- 3 + \frac{2}{n})}{n^{3} . (1 + \frac{2}{n^{2}} - \frac{1}{n^{3}})} = l i m \frac{- 3 + \frac{2}{n}}{n^{2} . (1 + \frac{2}{n^{2}} - \frac{1}{n^{3}})} = 0 4, l i m \frac{\sqrt{4 n^{2} + n + 1}}{1 - 2 n} = l i m \frac{n \sqrt{4 + \frac{1}{n} + \frac{1}{n^{2}}}}{n (\frac{1}{n} - 2)}, d o n > 0 = l i m \frac{\sqrt{4 + \frac{1}{n} + \frac{1}{n^{2}}}}{\frac{1}{n} - 2} = \frac{\sqrt{4}}{- 2} = - 1$ ..

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Answer 2

$1, l i m \frac{- 5 n + 3}{2 n - 6} = l i m \frac{n . (- 5 + \frac{3}{n})}{n (2 - \frac{6}{n})} = l i m \frac{- 5 + \frac{3}{n}}{2 - \frac{6}{n}} = - \frac{5}{2} 2, l i m \frac{2 n^{3} - 4 n^{2} + 3 n + 3}{n^{3} - 5 n + 7} = l i m \frac{n^{3} . (2 - \frac{4}{n} + \frac{3}{n^{2}} + \frac{3}{n^{3}})}{n^{3} . (1 - \frac{5}{n^{2}} + \frac{7}{n^{3}})} = l i m \frac{2 - \frac{4}{n} + \frac{3}{n^{2}} + \frac{3}{n^{3}}}{1 - \frac{5}{n^{2}} + \frac{7}{n^{3}}} = 2 3, l i m \frac{- 3 n + 2}{n^{3} + 2 n - 1} = l i m \frac{n . (- 3 + \frac{2}{n})}{n^{3} . (1 + \frac{2}{n^{2}} - \frac{1}{n^{3}})} = l i m \frac{- 3 + \frac{2}{n}}{n^{2} . (1 + \frac{2}{n^{2}} - \frac{1}{n^{3}})} = 0 4, l i m \frac{\sqrt{4 n^{2} + n + 1}}{1 - 2 n} = l i m \frac{n \sqrt{4 + \frac{1}{n} + \frac{1}{n^{2}}}}{n (\frac{1}{n} - 2)}, d o n > 0 = l i m \frac{\sqrt{4 + \frac{1}{n} + \frac{1}{n^{2}}}}{\frac{1}{n} - 2} = \frac{\sqrt{4}}{- 2} = - 1$ ..

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