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人気のある微分積分 >

limit as x approaches infinity of (e^{2x-7})/(6x)

解

x \to \infty lim (\frac{e ^{2 x - 7}}{6 x})

解

\infty

解答ステップ

x \to \infty lim (\frac{e ^{2 x - 7}}{6 x})

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

= \frac{1}{6} \cdot x \to \infty lim (\frac{e ^{2 x - 7}}{x})

簡素化

e^{2 x - 7} : e^{2 x} e^{- 7}

= \frac{1}{6} \cdot x \to \infty lim (\frac{e ^{2 x} e ^{- 7}}{x})

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

= \frac{1}{6} e^{- 7} \cdot x \to \infty lim (\frac{e ^{2 x}}{x})

指数の規則を適用する:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{6} \cdot \frac{1}{e ^{7}} \cdot x \to \infty lim (\frac{e ^{2 x}}{x})

ロピタルの定理を適用する

= \frac{1}{6} \cdot \frac{1}{e ^{7}} \cdot x \to \infty lim (\frac{e ^{2 x} \cdot 2}{1})

簡素化

= \frac{1}{6} \cdot \frac{1}{e ^{7}} \cdot x \to \infty lim (2 e^{2 x})

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

= \frac{1}{6} \cdot \frac{1}{e ^{7}} \cdot 2 \cdot x \to \infty lim (e^{2 x})

連鎖法則の制限を適用する:

\infty

= \frac{1}{6} \cdot \frac{1}{e ^{7}} \cdot 2 \cdot \infty

無限大の特性を適用する:

c \cdot \infty = \infty

= \infty

グラフ

人気の例

integral of (x^2-7)/(7x)

\int \frac{x ^{2} - 7}{7 x} d x

derivative 7e^xsqrt(x)

d er i v a t i v e 7 e^{x} x

limit as x approaches infinity of 25-2x

x \to \infty lim (25 - 2 x)

integral of 4/(xln(9x))

\int \frac{4}{x ln ( 9 x )} d x

integral of (3x^2-2x)

\int (3 x^{2} - 2 x) d x