再问一个！数学题呵呵

mossadUID: 183838

f(x) is differetiable, and when x->infinity,  f(x) and first derivative of f(x) have finite limit, then which must be true:

A) lim(x->infinity) f'(x)=0
B) lim (x->lnfinity)f''(x)=0

why A is correct, what is the idea? How about B? Thanks!:loveliness:

wangdxUID: 2270407

As my understanding, differetiable does not mean smooth, f'' might not exist~

hzw123UID: 2136905

how about f(x)=sinx ?

sunsydUID: 2393232

if lim(x->infinity) f'(x)=A>0, then for large x, f'(x)>A/2, then lim(x->infinity) f'(x)=infinity

yyl110UID: 2445192

sinx meijixian

yonkeUID: 2276888

i think maybe the f"(x)may not exist at all.

david.lUID: 2503791

明显是高数知识哦，

2314097UID: 2411431

f（x）有有限的极限说明，它的图像的在x->infinite 的时候应该是‘平’的，所以应该选A吧

QazCalyUID: 2487087

求和f(n+1)-f(n)=f(无穷)-f(k)=求和f'(an)  n<an<n+1   一般项趋于0  an就是x趋于无穷的子列  由极限的存在性的A