Proving Inequality: (6x^2 - 7sinx)/(3x+1) >1000

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Homework Help Overview

The discussion revolves around proving the inequality (6x^2 - 7sinx)/(3x+1) > 1000 for x > m and x > 0. Participants are exploring the implications of this inequality and attempting to manipulate it through various approximations and comparisons.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to simplify the original inequality by making approximations and comparing it to related expressions. There is a focus on manipulating the terms to find a clearer path to proving the inequality.

Discussion Status

The discussion is ongoing, with participants sharing their attempts at simplification and questioning the next steps. Some guidance has been offered regarding the implications of certain conditions, but there is no explicit consensus on how to proceed further.

Contextual Notes

Participants are working under the assumption that x > m and x > 0, with a specific interest in values of m that relate to the inequality being discussed.

nhrock3
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i have this question and solution
2rdb1ae.jpg

i have a similar question which i can't solve similarly

i need to prove
(6x^2 - 7sinx)/(3x+1) >1000 for x>m and x>0
(6x^2 - 7sinx)/(3x+1) >(6x^2 - 7)/(3x+1)

that as far as i could go
 
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Keep making approximations

(6x^2 - 7sinx)/(3x+1) >(6x^2 - 7)/(3x+1) > (6x^2 - 7sinx)/(3x+1) >(6x^2 - 7)/(3x+3x)

(6x^2 - 7)/(3x+3x) = (6x^2 -7)/6x = x -7/(6x)
 
(6x^2 - 7sinx)/(3x+1) >(6x^2 - 7)/(3x+3x)=x-7/x
what now
?
 
nhrock3 said:
(6x^2 - 7sinx)/(3x+1) >(6x^2 - 7)/(3x+3x)=x-7/x
what now
?

What do you mean "what now "? Are not capable of thinking for yourself ?

If you have something like

x - 7/x if x>M and M > 1008

then

x - 7/x > x -7 > 1008 -7 = 1001
 

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