limit as x approaches infinity of (3x-2)/(6x+1)

解答

x \to \infty lim (\frac{3 x - 2}{6 x + 1})

\frac{1}{2}

十进制

0.5

求解步骤

x \to \infty lim (\frac{3 x - 2}{6 x + 1})

除以分母的最高次幂:

\frac{3 - \frac{2}{x}}{6 + \frac{1}{x}}

= x \to \infty lim (\frac{3 - \frac{2}{x}}{6 + \frac{1}{x}})

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 _{x \to \infty} ( 3 - \frac{2}{x} )}{lim _{x \to \infty} ( 6 + \frac{1}{x} )}

x \to \infty lim (3 - \frac{2}{x}) = 3

x \to \infty lim (6 + \frac{1}{x}) = 6

= \frac{3}{6}

约分:

3

= \frac{1}{2}

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