Graph of y=(lnx)^2

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Droneon
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#1
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#1
Can someone explain why the graph of y=(lnx)^2 looks the way it does? I especially don't get why there's a slight curve where the graph meets the x-axis (x=1)
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Gatewaymerge
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What do you mean by there's a curve? Cause the graph of ln(x)^2 should be lnx with the negative values flipped and values squared, I think you're asking why does it look like a smooth curve at x=1? Probably because when you square numbers that are -1<x<1 they get smaller rather than bigger, so for the interval [1/e,1] and [1,e] the values will be smaller and for the rest they'll be bigger. Regardless you know that at x=1 is the minimum and the root and you also know the domain/range of ln(x)^2 and you also know the graph of ln(x) so there shouldn't really be any problem. However you draw it, with a spike at x=1 or a smooth curve you'll get the marks.
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DFranklin
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(Original post by Gatewaymerge)
What do you mean by there's a curve? Cause the graph of ln(x)^2 should be lnx with the negative values flipped and values squared, I think you're asking why does it look like a smooth curve at x=1? Probably because when you square numbers that are -1<x<1 they get smaller rather than bigger, so for the interval [1/e,1] and [1,e] the values will be smaller and for the rest they'll be bigger. Regardless you know that at x=1 is the minimum and the root and you also know the domain/range of ln(x)^2 and you also know the graph of ln(x) so there shouldn't really be any problem. However you draw it, with a spike at x=1 or a smooth curve you'll get the marks.
Possibly I'm harsh, but I would drop marks for a graph that doesn't show that the curve is smooth at x = 1. (ln x is smooth at x = 1, therefore (ln x)^2 is. This is reasonably fundamental I would have thought).
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arizonaidiot
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(Original post by Droneon)
Can someone explain why the graph of y=(lnx)^2 looks the way it does? I especially don't get why there's a slight curve where the graph meets the x-axis (x=1)
I'm also taking IAL and wondering if you could help me out.I'm taking the same subjects as you and have just started AS level.Can you tell me what book you used for biology,chemistry and physics.How many hours did you study from october vs nearer to the exams.What technique to you recommend I use if I want to achieve 4as in my AS year(I'm doing maths too).Also,should I use the green student book by ann fulick for biology?Which book is better for physics: Hodder or the red student book by miles hudson?
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Droneon
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(Original post by arizonaidiot)
I'm also taking IAL and wondering if you could help me out.I'm taking the same subjects as you and have just started AS level.Can you tell me what book you used for biology,chemistry and physics.How many hours did you study from october vs nearer to the exams.What technique to you recommend I use if I want to achieve 4as in my AS year(I'm doing maths too).Also,should I use the green student book by ann fulick for biology?Which book is better for physics: Hodder or the red student book by miles hudson?
I used the green book for biology, and for physics, both books are quite helpful, except that in the Hodders book, there are some unneeded content. Imnot exactly sure about the hours, but from IcT bed towards the end of the syllabus, I did all of my homework regularly, and also did some regular studying which helped me keep up with all the work so it didn't pile up towards the exams. This is esp important for maths, and if you're doing mechanics like I did, try to understand as much as possible, and once youredone with the five chaps, go straight to past papers and do as much as you can. The same g Es for all the subjects. Time it, do it, check your answers with the mark schemes, and don't be too lenient on yourself. It'll motivate you to do better each paper. Bio and Chem are ok if you get the theory and calculations straight. Theresess application. But physics is the opposite, esp unit 1. To get the hang of it, you need to do past papers and make sure you understand the situation in each question. If you don't, ask your teacher cuz it's very important that you do. And don't procrastinate. I did 4 subjects too in AS and got 3As and a B for bio, which was only two marks away from an A. But I'm not repeating any of the units cuz it's just two marks and I could work hard for it in A2, plus it would take away all of my attention from A2. I also got a full UMS in unit 1 of physics, which is tough to get if you don't practise enough.
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arizonaidiot
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#6
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(Original post by Droneon)
I used the green book for biology, and for physics, both books are quite helpful, except that in the Hodders book, there are some unneeded content. Imnot exactly sure about the hours, but from IcT bed towards the end of the syllabus, I did all of my homework regularly, and also did some regular studying which helped me keep up with all the work so it didn't pile up towards the exams. This is esp important for maths, and if you're doing mechanics like I did, try to understand as much as possible, and once youredone with the five chaps, go straight to past papers and do as much as you can. The same g Es for all the subjects. Time it, do it, check your answers with the mark schemes, and don't be too lenient on yourself. It'll motivate you to do better each paper. Bio and Chem are ok if you get the theory and calculations straight. Theresess application. But physics is the opposite, esp unit 1. To get the hang of it, you need to do past papers and make sure you understand the situation in each question. If you don't, ask your teacher cuz it's very important that you do. And don't procrastinate. I did 4 subjects too in AS and got 3As and a B for bio, which was only two marks away from an A. But I'm not repeating any of the units cuz it's just two marks and I could work hard for it in A2, plus it would take away all of my attention from A2. I also got a full UMS in unit 1 of physics, which is tough to get if you don't practise enough.
Thank you brother.It means alot that you took your time to write all that for me.Thanks alot.So the green book by ann fulick for biology is good enough for an A if done with pastpapers,right?
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Droneon
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#7
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#7
(Original post by arizonaidiot)
Thank you brother.It means alot that you took your time to write all that for me.Thanks alot.So the green book by ann fulick for biology is good enough for an A if done with pastpapers,right?
It's quite good, but don't depend completely on it, try to find extra notes from other sources through the Internet for example. And yeah, past papers are very important, cuz when you do lots of them, you get the hang of the pattern, and it gets easier.
You're welcome. Also, I'm a sister.
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arizonaidiot
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(Original post by Droneon)
It's quite good, but don't depend completely on it, try to find extra notes from other sources through the Internet for example. And yeah, past papers are very important, cuz when you do lots of them, you get the hang of the pattern, and it gets easier.
You're welcome. Also, I'm a sister.
Thank you once again.I'll be buying the green book for biology and the pearson revision guide and the hodder book for physics.Hope I made the right decision.Also,can I know your ums for both bio and physics?Once again,thanks alot,it's rare finding good and genuine people these days.
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Droneon
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#9
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#9
(Original post by arizonaidiot)
Thank you once again.I'll be buying the green book for biology and the pearson revision guide and the hodder book for physics.Hope I made the right decision.Also,can I know your ums for both bio and physics?Once again,thanks alot,it's rare finding good and genuine people these days.
Good luck! Phys 268, Bio 237
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Droneon
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#10
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#10
(Original post by arizonaidiot)
Thank you once again.I'll be buying the green book for biology and the pearson revision guide and the hodder book for physics.Hope I made the right decision.Also,can I know your ums for both bio and physics?Once again,thanks alot,it's rare finding good and genuine people these days.
The Hodders book has better explanations, so yes, you did.
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Droneon
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#11
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#11
(Original post by arizonaidiot)
Thank you once again.I'll be buying the green book for biology and the pearson revision guide and the hodder book for physics.Hope I made the right decision.Also,can I know your ums for both bio and physics?Once again,thanks alot,it's rare finding good and genuine people these days.
Aren't you doing chemistry?
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arizonaidiot
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(Original post by Droneon)
Aren't you doing chemistry?
I do chemistry but my sir is known to provide excellent notes so i'm not too bothered about that.Last year, many people got a's just by reading his notes and doing pastpapers.Also,great ums smart girl.
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arizonaidiot
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(Original post by Droneon)
Aren't you doing chemistry?
I keep bothering you so much but you used the green biology book from the 2008 specification right?or the one with biology b written on it?
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Droneon
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#14
(Original post by arizonaidiot)
I keep bothering you so much but you used the green biology book from the 2008 specification right?or the one with biology b written on it?
2008 specification, by Ann Fulick.
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arizonaidiot
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#15
(Original post by Droneon)
2008 specification, by Ann Fulick.

Do keep in touch .ImageI'm following you on tsr now.
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Droneon
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#16
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(Original post by arizonaidiot)
Do keep in touch .ImageI'm following you on tsr now.
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