数学极限题 求大佬

Question

如题所述

Answer 1

f(0-)=lim(x->0) { x[sin(1/x)]^2 +a } =a
f(0+)=f(0) =lim(x->0) (cosx -a )= 1-a
x=0, f(x)连续
a=1-a
a=1/2追问

lim(x->0) { x[sin(1/x)]^2 +a }怎么求呢 求步骤

追答

|[sin(1/x)]^2 |≤1
lim(x->0) x =0
=> lim(x->0) x[sin(1/x)]^2 =0
lim(x->0) { x[sin(1/x)]^2 +a } = 0+a= a

Answer 2