zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的微积分 >

limit as x approaches infinity+of (x^3)/(1e^{x/4)}

解答

x \to \infty + lim (\frac{x ^{3}}{1 e ^{\frac{x}{4}}})

解答

0

求解步骤

x \to \infty lim (\frac{x ^{3}}{1 \cdot e ^{\frac{x}{4}}})

化简

= x \to \infty lim (\frac{x ^{3}}{e ^{\frac{x}{4}}})

使用洛必达法则

= x \to \infty lim (\frac{3 x ^{2}}{e ^{\frac{x}{4}} \frac{1}{4}})

使用洛必达法则

= x \to \infty lim (\frac{6 x}{\frac{1}{16} e ^{\frac{x}{4}}})

使用洛必达法则

= x \to \infty lim (\frac{6}{\frac{1}{64} e ^{\frac{x}{4}}})

化简

\frac{6}{\frac{1}{64} e ^{\frac{x}{4}}} : \frac{384}{e ^{\frac{x}{4}}}

= x \to \infty lim (\frac{384}{e ^{\frac{x}{4}}})

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

= 384 \cdot x \to \infty lim (\frac{1}{e ^{\frac{x}{4}}})

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

不定型除外

= 384 \cdot \frac{lim _{x \to \infty} ( 1 )}{lim _{x \to \infty} ( e ^{\frac{x}{4}} )}

x \to \infty lim (1) = 1

x \to \infty lim (e^{\frac{x}{4}}) = \infty

= 384 \cdot \frac{1}{\infty}

化简

384 \cdot \frac{1}{\infty} : 0

= 0

作图

流行的例子

(\partial)/(\partial x)(x^{ey})

\frac{\partial}{\partial x} (x^{ey})

integral of 1/(x^2+3x+4)

\int \frac{1}{x ^{2} + 3 x + 4} d x

integral of 1/(81e^{-7x)+e^{7x}}

\int \frac{1}{81 e ^{- 7 x} + e ^{7 x}} d x

integral of ((x^2-4))/(x(x^2+4))

\int \frac{( x ^{2} - 4 )}{x ( x ^{2} + 4 )} d x

(\partial)/(\partial x)(y^2z)

\frac{\partial}{\partial x} (y^{2} z)