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Note that:x.(3+cosx)>2sinx , x>0 I should solve this problem with mean value theorem and I am not sure how to because of x>0 but not x>=0.

3 + cos(x) >= 2

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okay, after applying this I could show that sinx<x for x>0 and its done, thanksNote that:

3 + cos(x) >= 2

Please show us what you have tried andexactly where you are stuck.Please follow the rules of posting in this forum, as enunciated at:Please share your work/thoughts about this assignment.

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Maybe so, but you are required to use the mean value theorem.okay, after applying this I could show that sinx<x for x>0 and its done, thanks

I have a similiar question but this time that rule seems like can not help. Then how we can prove x.(2+cosx)>3sinxokay, after applying this I could show that sinx<x for x>0 and its done, thanks

yes, that's how I proved itMaybe so, but you are required to use the mean value theorem.

You cannot prove that because it is not true.I have a similiar question but this time that rule seems like can not help. Then how we can prove x.(2+cosx)>3sinx

\(\displaystyle 0\{2 + cos(0)\} = 0(2 + 1) = 0 * 3 = 0 \not > 0 = 3sin(0).\)

yes, sorry I didnt mention x>0 againYou cannot prove that because it is not true.

\(\displaystyle 0\{2 + cos(0)\} = 0(2 + 1) = 0 * 3 = 0 \not > 0 = 3sin(0).\)