anonymous
  • anonymous
How can I solve this for x? ... cos(pi*x) = 4x^2 - 1
Mathematics
schrodinger
  • schrodinger
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nincompoop
  • nincompoop
|dw:1439590609138:dw|
nincompoop
  • nincompoop
|dw:1439590681521:dw|
anonymous
  • anonymous
Ohhh but then how would you know that they intersect at those points (i mean at the x-intercepts) ?

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xapproachesinfinity
  • xapproachesinfinity
do intermediate value thm
anonymous
  • anonymous
Ohhh right right!! Can you help me out with it?
xapproachesinfinity
  • xapproachesinfinity
eh lol you want exact numbers that may not be a good way
anonymous
  • anonymous
No no haha not exact numbers xD lol just lead me in the right way and I'll take it from there
xapproachesinfinity
  • xapproachesinfinity
what i meant is that IVT that proves that in an interval there exist a solution not helpful to determine those solution so you need a different way as your question is asking to solve..
anonymous
  • anonymous
Hmm, well I'm actually trying to solve a different question but I need to find the intersection of the 2 graphs (y=cos(pi*x) and y=4x^2-1) in order to solve it... I'm looking for the area of the enclosed region.
xapproachesinfinity
  • xapproachesinfinity
enclosed region |dw:1439591365383:dw|
xapproachesinfinity
  • xapproachesinfinity
http://prntscr.com/84qa1x
anonymous
  • anonymous
Exactly! And I'm not sure how to find the intersection points of the 2 graphs... |dw:1439591506353:dw| I usually set the 2 equations to equal each other, but it doesn't work with this problem
anonymous
  • anonymous
Is there any way to find it without using a calculator?
xapproachesinfinity
  • xapproachesinfinity
yeah that work with simple equations lol
anonymous
  • anonymous
So not with this one?
xapproachesinfinity
  • xapproachesinfinity
i guess not with simple algebra no? could be with some advanced maneuver that uses calculus and different other stuff haha
xapproachesinfinity
  • xapproachesinfinity
yeah it is x=-+1/2 the graph shows the same
anonymous
  • anonymous
Ok, the thing is, I have a Calculus final exam in a couple days and I was wondering how to go about such a question cuz we're not allowed to use calculators either...
anonymous
  • anonymous
Refer to the attachment.
1 Attachment
anonymous
  • anonymous
But I guess in that case such a question wouldn't appear on an exam then, right?
xapproachesinfinity
  • xapproachesinfinity
i don't think you gonna have some problem of this sort without giving those points this needs some program haha
anonymous
  • anonymous
@robtobey it doesn't open the file :/
anonymous
  • anonymous
Haha good! Relief xD lol
xapproachesinfinity
  • xapproachesinfinity
you don;t have file opener of that time you need mathematica or something
xapproachesinfinity
  • xapproachesinfinity
of that type*
anonymous
  • anonymous
Yeah, whats mathematica?
xapproachesinfinity
  • xapproachesinfinity
a language or something hhh they solve problems with it i don't know either lol
anonymous
  • anonymous
Sorry. I intended to post a pdf file.
1 Attachment
xapproachesinfinity
  • xapproachesinfinity
http://prntscr.com/84qeo7
xapproachesinfinity
  • xapproachesinfinity
mathematica is an environment i guess right @robtobey
anonymous
  • anonymous
Now I see it :) thanks! That makes sense...
xapproachesinfinity
  • xapproachesinfinity
that was IVT usage by wolfram
anonymous
  • anonymous
I wish it showed the solution too, but I guess you gotta go pro for that XD haha
xapproachesinfinity
  • xapproachesinfinity
it has solution x=+-1/2 ?
anonymous
  • anonymous
yeah, i mean the step-by-step solution
xapproachesinfinity
  • xapproachesinfinity
what steps? how it used IVT?
anonymous
  • anonymous
mhmm
xapproachesinfinity
  • xapproachesinfinity
you could choose the interval [0,1] and do iterations of the thm or may be newtons method
xapproachesinfinity
  • xapproachesinfinity
that would lead to one solution close to 0.5 use symmetry then to get -0.5 that;s a lot of work
anonymous
  • anonymous
Hmm right, I'll give that try later on And yeah its a lots of work for just finding the intersection points to then finally get to work out the area between the 2 curves... it wouldn't be reasonable to get a question like this on the exam...
xapproachesinfinity
  • xapproachesinfinity
newton's method works good lead straight to the answer more quickly
anonymous
  • anonymous
Yeah, I gotta review that again, it was from last term and I tend to forget math really soon xD hahaha
anonymous
  • anonymous
But thank you all for the help! I appreciate it :)
xapproachesinfinity
  • xapproachesinfinity
i just use wolfram or any other program with this stuff in exam they will give you the intersection point if this sort of question pops up
anonymous
  • anonymous
Mhmm, hopefully it doesn't show up on the exam at all - just don't like it xD lol
xapproachesinfinity
  • xapproachesinfinity
lol depends on the prof
anonymous
  • anonymous
He's cruel and nice at the same time - pretty unpredictable xD haha
anonymous
  • anonymous
Anyways wish me luck! :D Im really nervous lol
xapproachesinfinity
  • xapproachesinfinity
yeah bonne chance :)
anonymous
  • anonymous
Merci beaucoup Monsieur ;D haha
xapproachesinfinity
  • xapproachesinfinity
de rien haha
anonymous
  • anonymous
lol
xapproachesinfinity
  • xapproachesinfinity
حظا سعيدا
anonymous
  • anonymous
Thats Arabic! :O haha awesome!
xapproachesinfinity
  • xapproachesinfinity
yeah it is :) Arabic is tough little bit
anonymous
  • anonymous
Yeah, I almost learned to speak it when I was little but then forgot it after a while of not working on it :/
anonymous
  • anonymous
But I still remember some words and can still read :D
xapproachesinfinity
  • xapproachesinfinity
oh good :) i understand french but i don't speak it fluently due to luck of practice too haha
anonymous
  • anonymous
Same here! I understand French and German a lot better than speaking them xD French, in particular, I've studied for over 6 years and yet can't speak it xD such a shame hahaha
xapproachesinfinity
  • xapproachesinfinity
eh what shame lol i studied french for over 14 years i even studied math with french but outside school i never practiced speaking it
anonymous
  • anonymous
anonymous
  • anonymous
Hahaha wow!! Lets just admit its a tough language xD
xapproachesinfinity
  • xapproachesinfinity
eh perhaps it is
xapproachesinfinity
  • xapproachesinfinity
eh haha forgot that
anonymous
  • anonymous
Mmhm it sure is xD lol
anonymous
  • anonymous
Lol
xapproachesinfinity
  • xapproachesinfinity
haha could be lack of interest too i never had intereest in it
anonymous
  • anonymous
Could be... But for me, it has always been a dream to be able to speak French - it just sounds so nice xD haha
xapproachesinfinity
  • xapproachesinfinity
haha language of romance restudy it xD
anonymous
  • anonymous
Lol true xD certainly does sound romantic xD and I definitely will... once my schedule gets a bit lighter xD lol
nincompoop
  • nincompoop
sorry I was at work so we can solve for their intersection points manually cos(pi*x) = 4x^2 - 1 means cos(pi x = 0 4x^2 -1 = 0
anonymous
  • anonymous
Refer to the attachment from the Mathematica 9 program. Sort of a proof for the first quadrant.
1 Attachment

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