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人気のある微分積分 >

limit as x approaches infinity of x*sin(7/x)

解

x \to \infty lim (x \cdot sin (\frac{7}{x}))

解

7

解答ステップ

x \to \infty lim (x sin (\frac{7}{x}))

ロピタル向けに書き換える

= x \to \infty lim (\frac{sin ( \frac{7}{x} )}{\frac{1}{x}})

ロピタルの定理を適用する

= x \to \infty lim \frac{- \frac{7 c o s ( \frac{7}{x} )}{x ^{2}}}{- \frac{1}{x ^{2}}}

簡素化

\frac{- \frac{7 c o s ( \frac{7}{x} )}{x ^{2}}}{- \frac{1}{x ^{2}}} : 7 cos (\frac{7}{x})

= x \to \infty lim (7 cos (\frac{7}{x}))

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

= 7 \cdot x \to \infty lim (cos (\frac{7}{x}))

連鎖法則の制限を適用する:

1

= 7 \cdot 1

簡素化

= 7

グラフ

人気の例

limit as x approaches 1 of (x^2-3)/(x-9)

x \to 1 lim (\frac{x ^{2} - 3}{x - 9})

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