limit as x approaches infinity of 6(1+1/x)^{x^2}

解答

x \to \infty lim (6 (1 + \frac{1}{x})^{x^{2}})

\infty

求解步骤

x \to \infty lim (6 (1 + \frac{1}{x})^{x^{2}})

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

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

使用指数运算法则

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

使用极限链式法则:

\infty

= 6 \cdot \infty

运用无穷大属性:

c \cdot \infty = \infty

= \infty

\frac{5 x ^{4}}{e ^{x}}

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

\int_{2}^{4} 16 - x^{2} d x

6 e^{2 t}

\frac{d}{d x} (sin^{2} (cos (x)))