一道高数题追加50分求助

Question

求解这道题如何做呢

Answer 1

简单分析一下即可，答案如图所示

Answer 2

ans : D
f(x)
=2-cosx ; x≤0
=√x+1 ; x>0
f(0)
=f(0-)
=lim(x->0-) (2-cosx)
=1
f(0+)
=lim(x->0+) (√x+1)
=1
f'(0-)
=lim(h->0) [ 2-cosh -f(0) ]/h
=lim(h->0) [ 1-cosh ]/h
=0
f'(0-)
=lim(h->0) [ √h+1 -f(0) ]/h
=lim(h->0) √h/h
不存在

Answer 3

答案D