• Mathematician Chat v. 3.999...
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Split it into partial fractions? I don't know I'm terrible at integrals.
[QUOTE=JohanGS;46260848]While we're at it; [IMG]http://latex.codecogs.com/gif.latex?%5Cint%20%5Cfrac%7Btan%5E3x%20+%20tan%20x%7D%7Btan%5E3%20x+3tan%5E2x+2tanx+6%7D%20dx[/IMG][/QUOTE] Just had a look at this, didn't solve it but reduced it to easy polynomial integrals. These are the steps you need to take: - Substitute t = tanx = > dt/dx = sec^2x - cos^2x + sin^2x = 1 => tan^2x + 1 = sec^2x - Combining above two, we see that dt/dx = 1 + t^2 => dx = dt / (1+t^2) - Use above to replace differential sign in the integral for your substiution. - That should cancel out a factor in the numerator simplifying it down to an easier integral. - Didn't get past here but looks like you can split the denominator using partial fractions (note the denominator has a root at t=-3, use long division to factorise the polynomial) Hope that gets you the answer.
Do you know inverse trig functions? Basically if [img]http://i.imgur.com/YfHHPxt.gif[/img], then [img]http://i.imgur.com/Z8gaglv.gif[/img] => [img]http://i.imgur.com/xSS7L7X.gif[/img] (You will probably have to justify the variable change by saying that arctan is a bijection.) You then replace the dx in there along with the multiple tan(s). You end up with: [img]http://i.imgur.com/WXxltOB.gif[/img] It's still really messy. Now I didn't go all the way through but I suppose you could do some partial fraction decomposition to try and simplify the integral. [editline]17th October 2014[/editline] You ninja motherfucker. [editline]17th October 2014[/editline] Just so I'm not completely useless, -3 is an "obvious" solution to the t^3+3t^2+2t+6=0 equation. That should allow you to factorize it into two poles for your decomposition by doing a simple euclidean division. [editline]17th October 2014[/editline] Okay so I did the math and the answer seems to be: [img]http://i.imgur.com/zRQpg82.gif[/img] I might have made a mistake. Either way this is quite disgusting.
Heh, ninja edited you too, sorry bro.
[QUOTE=JohanGS;46260300]Assistance, pls [IMG]http://latex.codecogs.com/gif.latex?%5Cint%20%5Cfrac%7Bsin%5E2x%7D%7Bcos%5E3x%7D%20dx[/IMG][/QUOTE] For this one, remember sin^2(x) = 1-cos^2(x) to get make the integrand sec^3(x) - sec(x). Split this into two integrals. If you don't already have the integral of sec^3(x), use integration by parts.
[QUOTE=Krinkels;46263530]For this one, remember sin^2(x) = 1-cos^2(x) to get make the integrand sec^3(x) - sec(x). Split this into two integrals. If you don't already have the integral of sec^3(x), use integration by parts.[/QUOTE] This is probably the method by which someone's expected to solve this in an introductory calculus course.
Yes, but the thing is we aren't really familiar with the secant functions.
To be honest I had no idea what sec or csc meant nor have I come across any occasion in my schooling where it would have been useful (nor do I see why it would be). It's literally just the inverse of cos and sin respectively. You can do any manipulation of trig identities using cos, sin (and tan for convenience).
[QUOTE=_Axel;46263894]To be honest I had no idea what sec or csc meant nor have I come across any occasion in my schooling where it would have been useful (nor do I see why it would be). It's literally just the inverse of cos and sin respectively. You can do any manipulation of trig identities using cos, sin (and tan for convenience).[/QUOTE] Yeah the French system (based on your flagdog) doesn't teach them. The British (and American from what I've seen) systems insisting on using them. It's pretty much for convenience to 'simplify' differentiating and integrating because you're no longer dealing with inverse function notation. I guess it makes it easier to teach to high school students since the product rule is simpler to apply than the quotient rule.
I'm currently on this question in my homework. [I]The price of Biomed Corp. shares began the same two-year period at $12, but fell 25% in each year. What was their overall percent decline in price?[/I] I've done something like this before, but I can't quite put my finger on it. At first I thought it was as simple as subtract 25% from 12, but I don't believe that's the correct process. What should I be getting from this? EDIT: Actually screw what I said, I read the question wrong. The answer is -43.75%
[QUOTE=JohanGS;46263839]Yes, but the thing is we aren't really familiar with the secant functions.[/QUOTE] just trig identities, you'll grow to memorize them, forget them, remember them again, yell KHAAAAAAAAAN really loud in the air, then forget them again [editline]18th October 2014[/editline] just be glad they don't get into hyperbolics my transport professor decided to throw us an example that required us using them to solve some differential equations, just because he wanted to scare us
[url=https://dl.dropboxusercontent.com/u/1470986/ASSIGNMENT%202%2C%20cont.pdf]Uniqueness proofs are weird.[/url] I asked my professor about the way I had this proof written, and it's good enough for him, but it feels almost cheating. It's not really direct or contrapositive, but it follows logic.
[QUOTE=WastedJamacan;46266176][url=https://dl.dropboxusercontent.com/u/1470986/ASSIGNMENT%202%2C%20cont.pdf]Uniqueness proofs are weird.[/url] I asked my professor about the way I had this proof written, and it's good enough for him, but it feels almost cheating. It's not really direct or contrapositive, but it follows logic.[/QUOTE] It's not like every proof has to fall neatly into these two slots. Anyway it counts as contradiction if you suppose the reciprocals are distinct. If I'm remembering this right all proofs by contradiction are equivalent to proofs by contrapositive.
[QUOTE=Sableye;46266163]just trig identities, you'll grow to memorize them, forget them, remember them again, yell KHAAAAAAAAAN really loud in the air, then forget them again [editline]18th October 2014[/editline] just be glad they don't get into hyperbolics my transport professor decided to throw us an example that required us using them to solve some differential equations, just because he wanted to scare us[/QUOTE] Hyperbolics aren't really that much harder than regular trig functions. You only have to remember a few rules and you can deduce all identities from normal trig identities.
[QUOTE=ZeFruitNazi;46258091]a question on hand-writing notes using mathematic notation: how important is it to have neat and tidy handwriting? i try hard to make everything correct but it takes time but writing it uglily is even worse so idk[/QUOTE] Late, I know, but as someone who's written exclusively in cursive since I can't remember when, I know most of my math teachers absolutely hated me in Calculus and Physics because of the use of R and S so often. On a plus side, though, they liked the fact that some of my small notations were occasionally pretty clear.
[QUOTE=_Axel;46267961]Hyperbolics aren't really that much harder than regular trig functions. You only have to remember a few rules and you can deduce all identities from normal trig identities.[/QUOTE] true, but ive only had 2 instances so far in engineering and math classes where i've had to use them, both of them being attempts to trick up students and confuse them
[QUOTE=Sableye;46274348]true, but ive only had 2 instances so far in engineering and math classes where i've had to use them, both of them being attempts to trick up students and confuse them[/QUOTE] The most practical usage I've seen of them is to express differential equation solutions in a kinda more readable manner, but you can just stick to exponentials for that anyway.
I have problems with induction... if you could have any advice in one line, what would it be? Especially inequality. It seems like there is hundred ways to prove something...
I'd say do lots of problems. Personally I tend to know a trick after I've seen it/worked it out. [IMG]http://latex.codecogs.com/gif.latex?%5Cbegin%7Bpmatrix%7D%201%20%26%200%20%261%20%5C%5C%202%20%26%201%20%26%200%5C%5C%201%26%7B-1%7D%20%261%20%5Cend%7Bpmatrix%7D[/IMG] I want to calculate the adjugate matrix but I can't seem to get it right, help?
What are you getting for the adjugate matrix? It would help to see where you're going wrong.
Well, (1,2) gets me 0 instead of -2 which I think it was supposed to be.
Tried for several hours to show that area of a particular phase-space region is a particular value and I ended up with Jacobi Elliptic Integrals. Welp.:suicide: Also has anyone had any experience with Galois Theory? I'm looking at subjects to pursue over the Christmas break and it looks pretty interesting.
I'm taking AS mathmatics at the moment and all of this terrifies me. Christ, sometimes I have to search up how to find the area of a triangle.
[QUOTE=AcidGravy;46312818]I'm taking AS mathmatics at the moment and all of this terrifies me. Christ, sometimes I have to search up how to find the area of a triangle.[/QUOTE] lol ya, last night i had to google "area under a parabola" because the formula my statics teacher used was crazy wrong
[QUOTE=Sableye;46315735]lol ya, last night i had to google "area under a parabola" because the formula my statics teacher used was crazy wrong[/QUOTE] why not use calculus?
So I just had a thought... Say you had a sequence of infinite numbers arranged randomly. But due to the infinite nature of the sequence it isn't random at all. Indeed it would have to be a repeating pattern due to the nature of an infinite sequence.
I'm sure this is a dumb question since you guys are talking about real math and shit but is there an easy way to evaluate limits without having to pull out a calculator and actually check what the limit is? Like if I'm trying to find out the limit of something relatively simple but still obnoxious like: [img]http://i.imgur.com/nBN0cDJ.gif[/img] I can do it but I have to make a dumb table and check as it approaches 7 from both directions and all that nonsense. Problem is I don't think we're allowed a calculator for our next test, and I have no idea how to do that without a calculator in a speedy fashion.
[QUOTE=Kyle902;46317347]So I just had a thought... Say you had a sequence of infinite numbers arranged randomly. But due to the infinite nature of the sequence it isn't random at all. Indeed it would have to be a repeating pattern due to the nature of an infinite sequence.[/QUOTE] What?
[QUOTE=Kyle902;46317347]So I just had a thought... Say you had a sequence of infinite numbers arranged randomly. But due to the infinite nature of the sequence it isn't random at all. Indeed it would have to be a repeating pattern due to the nature of an infinite sequence.[/QUOTE] But there's infinite random numbers to choose from.
[QUOTE=Remedial Math;46317385]I'm sure this is a dumb question since you guys are talking about real math and shit but is there an easy way to evaluate limits without having to pull out a calculator and actually check what the limit is? Like if I'm trying to find out the limit of something relatively simple but still obnoxious like: [img]http://i.imgur.com/nBN0cDJ.gif[/img] I can do it but I have to make a dumb table and check as it approaches 7 from both directions and all that nonsense. Problem is I don't think we're allowed a calculator for our next test, and I have no idea how to do that without a calculator in a speedy fashion.[/QUOTE] Notice that there is a factor of (x-7) on both the numerator and the denominator. Those two terms will cancel, leaving you with the limit of (x^2+7x+49) as x approaches 7. The trick with evaluating limits is to re-express or simplify it in an equivalent way that does not lead to indeterminate forms when evaluating the limit. Once you have simplified it in such a way, then direct substitution of the x-value usually suffices.
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