limit as x approaches 0+of (x+1)^{1/x}

解答

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

e

十进制

2.71828 \dots

求解步骤

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

使用指数运算法则

= x \to 0 + lim (e^{\frac{1}{x} l n (x + 1)})

使用极限链式法则:

e

= e

x \to 0 lim (\frac{x - arctan ( x )}{x ^{2} tan ( x )})

x \to a lim (f (x) + h (x))

x \to 5 lim (2 x - 1)

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

x \to \infty lim (\frac{2}{x} + 4)