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1. ### Prove that this function is nonnegative

Thanks so much I finally realized
2. ### Prove that this function is nonnegative

Yes I'm sorry. I don't know why I make such mistakes
3. ### Prove that this function is nonnegative

why x=3/2+πk is not a solution?
4. ### 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. ### Prove that this function is nonnegative

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

7. ### Prove that this function is nonnegative

I'm sorry I don't understand what you want to say
8. ### 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. ### Prove that this function is nonnegative

I can show that f(x)≥0 .
10. ### 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

yes
12. ### Prove that this function is nonnegative

That's exactly my problem. Don't see a reason that z> 0
13. ### Prove that this function is nonnegative

Yes but I can't use it in this course. In my course it is Calculus 2
14. ### 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.
15. ### 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?
16. ### 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
17. ### 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
18. ### 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
19. ### 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
20. ### 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

thanks
22. ### 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?
23. ### 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?
24. ### 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
25. ### 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
26. ### 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

Thanks
28. ### 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...
29. ### 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

Thanks