Question

设y=f(x)在[a,正无穷]上连续,且x趋于正无穷时,f(x)存在,证明:f在[a,正无穷]上有界

Answer 1

证明：x趋于正无穷时,f(x)存在,故存在b,b>a.当x》b时,|f(x)|《M1

又y=f(x)在[a,正无穷]上连续,当然在[a,b]上连续,故当x在区间[a,b]时,|f(x)|《M2

所以：|f(x)|《max{M1,M2}=M