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人気のある微分積分 >

limit as x approaches infinity of xsin((4pi)/x)

解

x \to \infty lim (x sin (\frac{4 π}{x}))

解

4 π

+1

十進法表記

12.56637 \dots

解答ステップ

x \to \infty lim (x sin (\frac{4 π}{x}))

ロピタル向けに書き換える

= x \to \infty lim (\frac{sin ( \frac{4 π}{x} )}{\frac{1}{x}})

ロピタルの定理を適用する

= x \to \infty lim \frac{- \frac{4 π c o s ( \frac{4 π}{x} )}{x ^{2}}}{- \frac{1}{x ^{2}}}

簡素化

\frac{- \frac{4 π c o s ( \frac{4 π}{x} )}{x ^{2}}}{- \frac{1}{x ^{2}}} : 4 π cos (\frac{4 π}{x})

= x \to \infty lim (4 π cos (\frac{4 π}{x}))

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

= 4 π \cdot x \to \infty lim (cos (\frac{4 π}{x}))

連鎖法則の制限を適用する:

1

= 4 π 1

簡素化

= 4 π

グラフ

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