Limits problemneed some help

1. Sep 9, 2008

jason_r

Show x<(or equal) xsin(1/x) <(or equal) -x if x<0

and -|x| <(or equal) xsin(1/x) <(or equal) |x| if x cant be 0

2. Sep 9, 2008

sutupidmath

Well, we know that sine and cosine are bounded right?

so $$|sin(a)|\leq 1$$ wich means that

$$-1\leq sina \leq 1$$ now in your first part replace a by 1/x than multiply both sides by x, since x is smaller than zero, your inequality sides switch. procede similarly in 2.