- #1
dontdisturbmycircles
- 592
- 3
Homework Statement
Show that sin x < x for all x > 0
The Attempt at a Solution
I thought I was pretty good at calculus so I have kinda been shifting my calc class onto the bottom of my todo list, but this mean value theorem problem is giving me some problems.
For x > 1, sin x [tex]\leq[/tex] 1 < x
This was my start... after about 25 minutes of thinking about how the mean value theorem could be applied I looked in the back.. (with much reluctance, trust me). They chose 2pi instead of 1 for the first part, that is likely significant but I am not getting thepoint. They then proceed to prove that (sinx)/(x) = cos(c) for some c in (0,2pi) and I can see that at that point c sin x< x since cos(c)[tex]\leq 1[/tex] but ONLY at that point c... I don't see how it proves it for the general case in that interval...
Last edited: