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人気のある微分積分 >

limit as x approaches 0+of x/(e^{-3/x)}

解

x \to 0 + lim (\frac{x}{e ^{- \frac{3}{x}}})

解

\infty

解答ステップ

x \to 0 + lim (\frac{x}{e ^{- \frac{3}{x}}})

簡素化

\frac{x}{e ^{- \frac{3}{x}}} : e^{\frac{3}{x}} x

= x \to 0 + lim (e^{\frac{3}{x}} x)

ロピタル向けに書き換える

= x \to 0 + lim (\frac{e ^{\frac{3}{x}}}{\frac{1}{x}})

ロピタルの定理を適用する

= x \to 0 + lim \frac{- \frac{3 e ^{\frac{3}{x}}}{x ^{2}}}{- \frac{1}{x ^{2}}}

簡素化

\frac{- \frac{3 e ^{\frac{3}{x}}}{x ^{2}}}{- \frac{1}{x ^{2}}} : 3 e^{\frac{3}{x}}

= x \to 0 + lim (3 e^{\frac{3}{x}})

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

= 3 \cdot x \to 0 + lim (e^{\frac{3}{x}})

連鎖法則の制限を適用する:

\infty

= 3 \cdot \infty

無限大の特性を適用する:

c \cdot \infty = \infty

= \infty

グラフ

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