limit as n approaches 1+of n/(ln(n))

解答

n \to 1 + lim (\frac{n}{ln ( n )})

\infty

求解步骤

n \to 1 + lim (\frac{n}{ln ( n )})

\frac{n}{ln ( n )} = n \frac{1}{ln ( n )}

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

x \to a lim [f (x) \cdot g (x)] = x \to a lim f (x) \cdot x \to a lim g (x)

不定型除外

= n \to 1 + lim (n) \cdot n \to 1 + lim (\frac{1}{ln ( n )})

n \to 1 + lim (n) = 1

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

= 1 \cdot \infty

运用无穷大属性:

c \cdot \infty = \infty

= \infty

x \to 1 - lim (ln (x) ln (x - 1))

x \to 0 lim (\frac{2}{sin ^{2} ( x )})

x \to 7 lim (\frac{4}{x - 7})

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

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