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#1 Re: Help Me ! » Algebraic Inequalities » 2016-07-21 07:24:03
Wow! Oh my gosh thank you thank you thank you thank you so much!!! You guys did more than I expected, thank you guys!
#2 Help Me ! » Algebraic Inequalities » 2016-07-21 03:18:40
- pineapple12
- Replies: 5
Hi,
Prove that
sqrt((2x^2 - 2x + 1) / 2) >=1/(x + 1/x)
for $0 < x < 1.$
This is the original problem. I'm trying to prove an intermediate inequality sqrt((2x^2 - 2x + 1) / 2) >= 1/2 >= 1/(x+1/x) .
I used AM-GM on x + 1/x, and I ended up with 1/(x + 1/x) <= 1/2.
Now, I'm kind of having trouble finding a way to prove that sqrt((2x^2 - 2x + 1) / 2) >= 1/2. I don't know if I should use a mean inequality or what to do. I'm so close to solving this problem, so any strong hints would be appreciated.
Thank you so much!!! 
#3 Re: Help Me ! » Algebra Functions » 2016-06-26 05:06:31
So, is it decreasing??? There's not a line in the graph that increases although I'm not sure.
Also, I was wrong about the graph being neither even or odd, and not invertible either. 
Not sure what I did wrong.
Sorry...
Thanks anyway
#4 Re: Help Me ! » Algebra Functions » 2016-06-24 01:50:43
I see that for every interval, as x increases, the graph decreases. And, at every whole number, the graph just starts over and decreases again. Thanks so much for the graph!!!
Ok, so I think the graph is neither even or odd, and not invertible either. I'm not sure if it's increasing or decreasing though....
I cannot thank you enough! Thanks!
#5 Help Me ! » Algebra Functions » 2016-06-23 01:17:02
- pineapple12
- Replies: 5
Define {x} = x- \lfloor x\rfloor. That is to say, {x} is the "fractional part" of x. If you were to expand the number x as a decimal, {x} is the stuff after the decimal point. For example {3/2} = 0.5 and {\pi} = 0.14159...
Now, using the above definition, determine if the function below is increasing, decreasing, even, odd, and/or invertible on its natural domain:
f(x) = \lfloor x \rfloor - {x}
I'm kind of stuck on this one as I usually use a graph to help me determine if the function is increasing, decreasing, even, odd, etc. (oops, I know it's not a very reliable way) and for this one I have no idea what the graph would look like because of that floor function. How should I do this problem?
Any help would be appreciated! Thanks!
#6 Re: Help Me ! » 3d plane in a cube » 2016-06-23 01:04:18
@rileywkong Haha, thanks. I actually ended up using those triangles instead because the solution was shorter and easier in my opinion.
#7 Re: Help Me ! » 3d plane in a cube » 2016-06-21 07:33:29
Oh yeah... ok THANKS SO MUCH!!! 
#8 Re: Help Me ! » 3d plane in a cube » 2016-06-21 06:26:52
How do we know triangles SAQ and SDR are similar? (I hope I have my diagram correct) So, is SR a straight line and if it is, how do we know that? To be clear, point S is created when we extend CP and AD right??? Thank you in advance!
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