limit as x approaches-infinity of (5x^4+e^{5x})/(x^4)

解答

x \to - \infty lim (\frac{5 x ^{4} + e ^{5 x}}{x ^{4}})

5

求解步骤

x \to - \infty lim (\frac{5 x ^{4} + e ^{5 x}}{x ^{4}})

从

5 x^{4} + e^{5 x}

分解出因式

5 x^{4}

5 x^{4} (1 + \frac{e ^{5 x}}{5 x ^{4}})

= x \to - \infty lim \frac{5 x ^{4} ( 1 + \frac{e ^{5 x}}{5 x ^{4}} )}{x ^{4}}

化简

\frac{5 x ^{4} ( 1 + \frac{e ^{5 x}}{5 x ^{4}} )}{x ^{4}} : \frac{e ^{5 x}}{x ^{4}} + 5

= x \to - \infty lim (\frac{e ^{5 x}}{x ^{4}} + 5)

x \to a lim [f (x) \pm g (x)] = x \to a lim f (x) \pm x \to a lim g (x)

不定型除外

= x \to - \infty lim (\frac{e ^{5 x}}{x ^{4}}) + x \to - \infty lim (5)

x \to - \infty lim (\frac{e ^{5 x}}{x ^{4}}) = 0

x \to - \infty lim (5) = 5

= 0 + 5

化简

= 5

s l o p e (4 x + 4 y)^{3} = 64 x^{3} + 64 y^{3}

\int 9 e^{2 x + e^{2 x}} d x

\frac{d}{d x} (- 4 x^{\frac{1}{4}} + 3 x^{- 6})

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\frac{d y}{d t} = 0.75 y - 0.00003 y^{2}