题目

limx^αcos(1/x) 当x趋近于0+时候的极限
当α的取值范围为多少时，y=（x^α）cos(1/x)在x=0处的导数为0

提问时间：2020-08-10

答案

lim(x->0+) x^α .cos(1/x)
|cos(1/x)|≤1
=> lim(x->0+) x^α .cos(1/x) =0
f(x)=x^α .cos(1/x)
f(0) =0
f'(0) = lim(h->0)[ f(h) -f(0)]/ h
for α ≥ 1
f'(0) = lim(h->0) h^(α-1)cos(1/h) = 0