limit as t approaches infinity of (0.2t)/(t^2+1)

解

t \to \infty lim (\frac{0.2 t}{t ^{2} + 1})

0

解答ステップ

t \to \infty lim (\frac{0.2 t}{t ^{2} + 1})

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

= 0.2 \cdot t \to \infty lim (\frac{t}{t ^{2} + 1})

最高の分母べき乗で割る:

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

= 0.2 \cdot t \to \infty lim (\frac{\frac{1}{t}}{1 + \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

= 0.2 \cdot \frac{lim _{t \to \infty} ( \frac{1}{t} )}{lim _{t \to \infty} ( 1 + \frac{1}{t ^{2}} )}

t \to \infty lim (\frac{1}{t}) = 0

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

= 0.2 \cdot \frac{0}{1}

簡素化

0.2 \cdot \frac{0}{1} : 0

= 0