limit as y approaches-infinity of (2-y)/(sqrt(7+6y^2))

解

y \to - \infty lim (\frac{2 - y}{7 + 6 y ^{2}})

\frac{1}{6}

十進法表記

0.40824 \dots

解答ステップ

y \to - \infty lim (\frac{2 - y}{7 + 6 y ^{2}})

最高の分母べき乗で割る:

\frac{\frac{2}{y} - 1}{- \frac{7}{y ^{2}} + 6}

= y \to - \infty lim \frac{\frac{2}{y} - 1}{- \frac{7}{y ^{2}} + 6}

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

= - y \to - \infty lim \frac{\frac{2}{y} - 1}{\frac{7}{y ^{2}} + 6}

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{lim _{y \to - \infty} ( \frac{2}{y} - 1 )}{lim _{y \to - \infty} ( \frac{7}{y ^{2}} + 6 )}

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

y \to - \infty lim (\frac{7}{y ^{2}} + 6) = 6

= - \frac{- 1}{6}

簡素化

= \frac{1}{6}