limit as n approaches infinity of (2n+1)/(1-3sqrt(n))

解答

n \to \infty lim (\frac{2 n + 1}{1 - 3 n})

- \infty

求解步骤

n \to \infty lim (\frac{2 n + 1}{1 - 3 n})

Divide by

n : \frac{2 n + \frac{1}{n}}{\frac{1}{n} - 3}

= n \to \infty lim (\frac{2 n + \frac{1}{n}}{\frac{1}{n} - 3})

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

不定型除外

= \frac{lim _{n \to \infty} ( 2 n + \frac{1}{n} )}{lim _{n \to \infty} ( \frac{1}{n} - 3 )}

n \to \infty lim (2 n + \frac{1}{n}) = \infty

n \to \infty lim (\frac{1}{n} - 3) = - 3

= \frac{\infty}{- 3}

运用无穷大属性:

\frac{\infty}{- c} = - \infty

= - \infty

x \to 0 lim (\frac{ln ( 10 x + 1 )}{x})

x \to 0 lim (1 - \frac{tan ( 3 x )}{x})

x \to 4 + lim (10 - 2 x)

x \to - 2 lim (\frac{3}{( x + 2 ) ^{2}})

x \to 0 + lim (x^{2} (ln (x))^{2})