limit as x approaches infinity of 1/(x(ln(x))^4)

解答

x \to \infty lim (\frac{1}{x ( ln ( x ) ) ^{4}})

0

求解步骤

x \to \infty lim (\frac{1}{x ( ln ( x ) ) ^{4}})

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} ( 1 )}{lim _{x \to \infty} ( x ( ln ( x ) ) ^{4} )}

x \to \infty lim (1) = 1

x \to \infty lim (x (ln (x))^{4}) = \infty

= \frac{1}{\infty}

运用无穷大属性:

\frac{c}{\infty} = 0

= 0