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人気のある微分積分 >

limit as n approaches infinity of n/6 sin(6/n)

解

n \to \infty lim (\frac{n}{6} sin (\frac{6}{n}))

解

1

解答ステップ

n \to \infty lim (\frac{n}{6} sin (\frac{6}{n}))

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

= \frac{1}{6} \cdot n \to \infty lim (n sin (\frac{6}{n}))

ロピタル向けに書き換える

= \frac{1}{6} \cdot n \to \infty lim (\frac{sin ( \frac{6}{n} )}{\frac{1}{n}})

ロピタルの定理を適用する

= \frac{1}{6} \cdot n \to \infty lim \frac{- \frac{6 c o s ( \frac{6}{n} )}{n ^{2}}}{- \frac{1}{n ^{2}}}

簡素化

\frac{- \frac{6 c o s ( \frac{6}{n} )}{n ^{2}}}{- \frac{1}{n ^{2}}} : 6 cos (\frac{6}{n})

= \frac{1}{6} \cdot n \to \infty lim (6 cos (\frac{6}{n}))

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

= \frac{1}{6} \cdot 6 \cdot n \to \infty lim (cos (\frac{6}{n}))

連鎖法則の制限を適用する:

1

= \frac{1}{6} \cdot 6 \cdot 1

簡素化

\frac{1}{6} \cdot 6 \cdot 1 : 1

= 1

グラフ

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