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Ohhh but then how would you know that they intersect at those points (i mean at the x-intercepts) ?
do intermediate value thm
Ohhh right right!! Can you help me out with it?
eh lol you want exact numbers that may not be a good way
No no haha not exact numbers xD lol just lead me in the right way and I'll take it from there
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..
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.
enclosed region |dw:1439591365383:dw|
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
Is there any way to find it without using a calculator?
yeah that work with simple equations lol
So not with this one?
i guess not with simple algebra no? could be with some advanced maneuver that uses calculus and different other stuff haha
yeah it is x=-+1/2 the graph shows the same
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...
But I guess in that case such a question wouldn't appear on an exam then, right?
i don't think you gonna have some problem of this sort without giving those points this needs some program haha
@robtobey it doesn't open the file :/
Haha good! Relief xD lol
you don;t have file opener of that time you need mathematica or something
of that type*
Yeah, whats mathematica?
a language or something hhh they solve problems with it i don't know either lol
mathematica is an environment i guess right @robtobey
Now I see it :) thanks! That makes sense...
that was IVT usage by wolfram
I wish it showed the solution too, but I guess you gotta go pro for that XD haha
it has solution x=+-1/2 ?
yeah, i mean the step-by-step solution
what steps? how it used IVT?
you could choose the interval [0,1] and do iterations of the thm or may be newtons method
that would lead to one solution close to 0.5 use symmetry then to get -0.5 that;s a lot of work
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...
newton's method works good lead straight to the answer more quickly
Yeah, I gotta review that again, it was from last term and I tend to forget math really soon xD hahaha
But thank you all for the help! I appreciate it :)
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
Mhmm, hopefully it doesn't show up on the exam at all - just don't like it xD lol
lol depends on the prof
He's cruel and nice at the same time - pretty unpredictable xD haha
Anyways wish me luck! :D Im really nervous lol
yeah bonne chance :)
Merci beaucoup Monsieur ;D haha
de rien haha
Thats Arabic! :O haha awesome!
yeah it is :) Arabic is tough little bit
Yeah, I almost learned to speak it when I was little but then forgot it after a while of not working on it :/
But I still remember some words and can still read :D
oh good :) i understand french but i don't speak it fluently due to luck of practice too haha
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
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
Hahaha wow!! Lets just admit its a tough language xD
eh perhaps it is
eh haha forgot that
Mmhm it sure is xD lol
haha could be lack of interest too i never had intereest in it
Could be... But for me, it has always been a dream to be able to speak French - it just sounds so nice xD haha
haha language of romance restudy it xD
Lol true xD certainly does sound romantic xD and I definitely will... once my schedule gets a bit lighter xD lol
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