limit as x approaches infinity of (e^{3x-8})/(5x)

解答

x \to \infty lim (\frac{e ^{3 x - 8}}{5 x})

\infty

求解步骤

x \to \infty lim (\frac{e ^{3 x - 8}}{5 x})

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

= \frac{1}{5} \cdot x \to \infty lim (\frac{e ^{3 x - 8}}{x})

使用洛必达法则

= \frac{1}{5} \cdot x \to \infty lim (\frac{e ^{3 x - 8} \cdot 3}{1})

化简

= \frac{1}{5} \cdot x \to \infty lim (3 e^{3 x - 8})

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

= \frac{1}{5} \cdot 3 \cdot x \to \infty lim (e^{3 x - 8})

使用极限链式法则:

\infty

= \frac{1}{5} \cdot 3 \cdot \infty

运用无穷大属性:

c \cdot \infty = \infty

= \infty

\int (- x + 3) d x

\frac{\partial}{\partial x} (arctan (\frac{z}{x}))

y^{^{''}} - 10 y^{^{'}} + 50 y = 0, y (0) = 5, y^{^{'}} (0) = - 2

5 y^{^{''}} + 30 y = 0, y (0) = 5, y^{^{'}} (0) = 5

\int \frac{1}{a ^{2} + u ^{2}} d u