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

解答

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

e^{\frac{3}{4}}

十进制

2.11700 \dots

求解步骤

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

使用指数运算法则

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

使用极限链式法则:

e^{\frac{3}{4}}

= e^{\frac{3}{4}}

\int \frac{( ln ( x ^{2} ) )}{x} d x

d er i v a t i v e h (t) = (t + 5)^{\frac{2}{3}} (3 t^{2} - 1)^{3}

t an g e n t y = sin (4 x)

\int (cos (x))^{3} sin (x) d x

\int_{0}^{3} ((30 - y) - y^{\frac{1}{3}}) d y