答:
仅给出了分段函数,怎么求a和b啊?
应该有条件说f(x)是连续函数之类的才能求a和b
x<0,f(x)=tanx /x
x=0,f(x)=a
x>0,f(x)=xsin(1/x)+b
lim(x→0-) f(x)
=lim(x→0-) tanx /x
=lim(x→0-) x/x
=1
lim(x→0+)f(x)
=lim(x→0+) xsin(1/x) +b sin(1/x)有界,x为无穷小
=0+b
=b
因为:f(x)在x=0处连续
所以:a=b=1
答:
仅给出了分段函数,怎么求a和b啊?
应该有条件说f(x)是连续函数之类的才能求a和b
x<0,f(x)=tanx /x
x=0,f(x)=a
x>0,f(x)=xsin(1/x)+b
lim(x→0-) f(x)
=lim(x→0-) tanx /x
=lim(x→0-) x/x
=1
lim(x→0+)f(x)
=lim(x→0+) xsin(1/x) +b sin(1/x)有界,x为无穷小
=0+b
=b
因为:f(x)在x=0处连续
所以:a=b=1