第二小题怎么做,要过程,谢谢

2025-06-21 07:56:17
推荐回答(2个)
回答1:

n>√97也就是n=10时,
f(n)=1-(√98-√97)/(n-√97),
f(10)≤f(n)<1
1≤n<10时,
f(n)=1+(√98-√97)/(√97-n),
1所以最大值f(9),最小值f(10)

回答2:

fn=(n-98^0.5)/(n-97^0.5)=1+(97^0.5-98^0.5)/(n-97^0.5),可以看出,当n>10时,
(n-97^0.5)>10-97^0.5,
-(n-97^0.5)<-(10-97^0.5),
-1/(n-97^0.5)>-1/(10-97^0.5),两边同乘以98^0.5-97^0.5
(97^0.5-98^0.5)/(n-97^0.5)>(97^0.5-98^0.5)/(10-97^0.5),
1+(97^0.5-98^0.5)/(n-97^0.5)>1+(97^0.5-98^0.5)/(10-97^0.5),
当0-(n-97^0.5)>=-(9-97^0.5),
-1/(n-97^0.5)<=-1/(9-97^0.5),两边同乘以98^0.5-97^0.5
(97^0.5-98^0.5)/(n-97^0.5)<=(97^0.5-98^0.5)/(9-97^0.5),
1+(97^0.5-98^0.5)/(n-97^0.5)<=1+(97^0.5-98^0.5)/(9-97^0.5),
1+(97^0.5-98^0.5)/(10-97^0.5)gn同样用不等式推论