limit as x approaches 1 of x^{2/(x-1)}

解答

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

e^{2}

十进制

7.38905 \dots

求解步骤

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

使用指数运算法则

= x \to 1 lim (e^{\frac{2}{x - 1} l n (x)})

使用极限链式法则:

e^{2}

= e^{2}

x \to - 4 lim (\frac{1}{( x + 4 ) ^{2}})

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

x \to \frac{π}{2} lim ((2 x - π) tan (x))

x \to 1 + lim (tan (x - 1))

x \to 4 lim (\frac{2 x - 4}{x - 1})