limit as t approaches infinity of (ln(3t))/(t^2)

解

t \to \infty lim (\frac{ln ( 3 t )}{t ^{2}})

0

解答ステップ

t \to \infty lim (\frac{ln ( 3 t )}{t ^{2}})

ロピタルの定理を適用する

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

簡素化

\frac{\frac{1}{t}}{2 t} : \frac{1}{2 t ^{2}}

= t \to \infty lim (\frac{1}{2 t ^{2}})

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

= \frac{1}{2} \cdot t \to \infty lim (\frac{1}{t ^{2}})

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

不定形式の場合を除く

= \frac{1}{2} \cdot \frac{lim _{t \to \infty} ( 1 )}{lim _{t \to \infty} ( t ^{2} )}

t \to \infty lim (1) = 1

t \to \infty lim (t^{2}) = \infty

= \frac{1}{2} \cdot \frac{1}{\infty}

簡素化

\frac{1}{2} \cdot \frac{1}{\infty} : 0

= 0