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  1. sergey_le

    Prove that this function is nonnegative

    Thanks so much I finally realized
  2. sergey_le

    Prove that this function is nonnegative

    Yes I'm sorry. I don't know why I make such mistakes
  3. sergey_le

    Prove that this function is nonnegative

    why x=3/2+πk is not a solution?
  4. sergey_le

    Prove that this function is nonnegative

    Yes I know how to solve it x(1 + sin(x)) = 0 when x=0 or x=3/2+πk
  5. sergey_le

    Prove that this function is nonnegative

    You mean I have to show that there is no f' axis with x axis?
  6. sergey_le

    Prove that this function is nonnegative

    nothing special. Please direct me
  7. sergey_le

    Prove that this function is nonnegative

    I'm sorry I don't understand what you want to say
  8. sergey_le

    Prove that this function is nonnegative

    Also the derivative f'(x)≥0 I don't understand what you want me to do? How do I show that f'(x)>0 And no ≥
  9. sergey_le

    Prove that this function is nonnegative

    I can show that f(x)≥0 .
  10. sergey_le

    Prove that this function is nonnegative

    If I use contradiction, So I have to assume that f(a)≤0 , And I don't see a reason why that f(a)=0
  11. sergey_le

    Prove that this function is nonnegative

    That's exactly my problem. Don't see a reason that z> 0
  12. sergey_le

    Prove that this function is nonnegative

    Yes but I can't use it in this course. In my course it is Calculus 2
  13. sergey_le

    Prove that this function is nonnegative

    If that was the case then I had no problem . But because it is ≤ Then there is the possibility that f'(x)=0.
  14. sergey_le

    Prove that this function is nonnegative

    No That's what I intended to do. But my problem is with the one that can be x∈(0,δ) (when are δ>0) so that f'(x)=0 and then f(0)=f(x)=0 for ∀x∈(0,δ) And then what I have to prove is wrong. Do you understand my problem?
  15. sergey_le

    Prove that this function is nonnegative

    What I wanted to do was set f(x)=##x^2##/2 - xcosx+sinx And show that f(x)>0. f'(x)=x(1+sinx) First I wanted to prove that f(x)<0 in the interval (0,∞) 0≤1+sinx≤2 And thus for all x> 0 f'(x)≥0 and therefore f(x)≥f(0)=0 And it doesn't help me much because I need to f(x)>0
  16. sergey_le

    Let a_n be sequence so that a_n+1-a_n>-1 and |a_n|>2 for all n.

    Well thank you very much I will try to find a solution already. Thanks also for your patience
  17. sergey_le

    Let a_n be sequence so that a_n+1-a_n>-1 and |a_n|>2 for all n.

    I meant what you wrote here. If you don't understand what I wrote, tell me and I'll upload a photo of the inequality. Because I can't post it with the forum tools
  18. sergey_le

    Let a_n be sequence so that a_n+1-a_n>-1 and |a_n|>2 for all n.

    I'm sorry I didn't write the problem to the end. Yes I meant it #<## a_n+1##<##\frac a_n a_1 ## Prove that if for every n is Happening ## a_n+1##<##\frac a_n a_1 ## then a1<0
  19. sergey_le

    Let a_n be sequence so that a_n+1-a_n>-1 and |a_n|>2 for all n.

    hiii :smile: If you can help me with this problem I would be very happy
  20. sergey_le

    Let a_n be sequence so that a_n+1-a_n>-1 and |a_n|>2 for all n.

    Yes it is clear. Do you want me to re-post the question or understand what I'm asking?
  21. sergey_le

    Let a_n be sequence so that a_n+1-a_n>-1 and |a_n|>2 for all n.

    I tried to use https://www.physicsforums.com/help/latexhelp/ . But it didn't work, Maybe my question is clearer now?
  22. sergey_le

    Let a_n be sequence so that a_n+1-a_n>-1 and |a_n|>2 for all n.

    I need help only in section 3 I have some kind of solution but I'm not sure because it seems too short and too simple. We showed in section 1 that an> 0 per n. it Given that a_n + 1 <0 and a_n+1<\frac a_n a_1 In addition therefore a_1 <0 is warranted
  23. sergey_le

    Proving inequalities for these Sequences

    Ok I will read it and post my question again. I know it's hard to understand me either because my English is not good. Thank you for everything
  24. sergey_le

    Proving inequalities for these Sequences

    I need help only in section 3 I have some kind of solution but I'm not sure because it seems too short and too simple. We showed in section 1 that an> 0 per n. Given that an + 1 <0 and an + 1 = an / a1 therefore a1 <0 is warranted
  25. sergey_le

    Rolle's theorem

    Ok, I sort of understand what you want me to do. You want me to divide the interval [a,b] Into two parts With the help of a midpoint c. And say that For any t that is between f(a) and f(c) Exists x1∈[a,c] so that f(x1)=t , Then switch the point f(a) whit f(b) And say that ∃x2∈[c,b] so that...
  26. sergey_le

    Rolle's theorem

    It all makes sense to me, but I don't know how to formalize it nicely. I wanted to divide it into two cases. First case where f is fixed in the segment. And a second case where f is not fixed in the segment. But I don't know how to prove it for the case where f i is not fixed
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