指出函数f(x)=(x^-x)/(x^2-1)的间断点及其类型

Question

指出函数f(x)=(x^-x)/(x^2-1)的间断点及其类型

Answer 1

f(x) = (x²-x)/(x²-1)
分母不为零,x²-1≠0
x≠-1,x≠1
间断点两个：x1=-1,x2=1
(x²-x)/(x²-1) = x(x-1)/{(x+1)(x-1)} = x/(x+1)
x=1是可去除间断点,属于第一类间断点；
x=-1是无穷间断点,属于第二类间断点.