ja

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

人気のある微分積分 >

limit as x approaches infinity of ((e^{(15)/x}-1))/((15)/x)

解

x \to \infty lim \frac{( e ^{\frac{15}{x}} - 1 )}{\frac{15}{x}}

解

1

解答ステップ

x \to \infty lim (\frac{e ^{\frac{15}{x}} - 1}{\frac{15}{x}})

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

= \frac{1}{15} \cdot x \to \infty lim (\frac{e ^{\frac{15}{x}} - 1}{\frac{1}{x}})

簡素化

= \frac{1}{15} \cdot x \to \infty lim (x (e^{\frac{15}{x}} - 1))

ロピタル向けに書き換える

= \frac{1}{15} \cdot x \to \infty lim (\frac{- 1 + e ^{\frac{15}{x}}}{\frac{1}{x}})

ロピタルの定理を適用する

= \frac{1}{15} \cdot x \to \infty lim \frac{- \frac{15 e ^{\frac{15}{x}}}{x ^{2}}}{- \frac{1}{x ^{2}}}

簡素化

\frac{- \frac{15 e ^{\frac{15}{x}}}{x ^{2}}}{- \frac{1}{x ^{2}}} : 15 e^{\frac{15}{x}}

= \frac{1}{15} \cdot x \to \infty lim (15 e^{\frac{15}{x}})

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

= \frac{1}{15} \cdot 15 \cdot x \to \infty lim (e^{\frac{15}{x}})

連鎖法則の制限を適用する:

1

= \frac{1}{15} \cdot 15 \cdot 1

簡素化

\frac{1}{15} \cdot 15 \cdot 1 : 1

= 1

グラフ

人気の例

inverselaplace (s+3/2)^2

in v erse l a pl a ce (s + \frac{3}{2})^{2}

integral of e^{(-x)/k}*(-x)/k

\int e^{\frac{- x}{k}} \cdot \frac{- x}{k} d x

limit as x approaches infinity of x^3-2x

x \to \infty lim (x^{3} - 2 x)

derivative f(x)=(2x+5)/(x+2)*2x-5

d er i v a t i v e f (x) = \frac{2 x + 5}{x + 2} \cdot 2 x - 5

(dy)/(dx)=xy+y^2

\frac{d y}{d x} = x y + y^{2}