How Do Limits and Boundedness Apply to Trigonometric Functions?

jason_r · Sep 9, 2008

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 · Sep 9, 2008

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

so [tex]|sin(a)|\leq 1[/tex] which means that

[tex]-1\leq sina \leq 1[/tex] 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.

How Do Limits and Boundedness Apply to Trigonometric Functions?

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