How Do Limits and Boundedness Apply to Trigonometric Functions?

[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 can't be 0

 

[sutupidmath]

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

so |sin(a)|\leq 1 which 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.