lim（x趋向于1）5^(1/(x-1))极限为啥不存在且不是无穷大?

Question

lim（x趋向于1）5^(1/(x-1))极限为啥不存在且不是无穷大?

Answer 1

左右极限不同.
lim（x趋向于1）,5^(1/(x-1))左极限=1
lim（x趋向于1）,5^(1/(x-1))右极限=正无穷大
所以,limx趋向于1时,5^(1/(x-1))极限不存在.