limit as x approaches-infinity of 3xe^x

解答

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

0

求解步骤

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

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

= 3 \cdot x \to - \infty lim (x e^{x})

改写以应用洛必达法则

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

使用洛必达法则

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

化简

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

= 3 \cdot x \to - \infty lim (- e^{x})

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

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

运用一般极限法则:

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

= 3 (- 0)

化简

= 0

x \to 2 lim (\frac{x + 1}{x + 2})

x \to 1 lim (arccos (\frac{1}{x + 1}))

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

x \to 2 lim (6 x^{2} + 3 x - 9)

x \to - 2 + lim (\frac{x ^{2} + 1}{x + 2})