[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] That particular problem has already been simplified significantly. Notice that you have an (x-7) in both the numerator and denominator. These clearly cancel leaving you with only (x^2+7x+49), which you can evaluate by just plugging in the value you're taking the limit to. The trickiest part to most limit problems is really just factoring. If you end up calculating an indeterminate form such as 0/0, you need to find a way to factor out the term in the denominator that's giving you trouble.
[editline]October 2014[/editline]
what he said
[qUOTE=PopLot;46317899]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.[/quote]
[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]
An infinite string of numbers does not have to be repeating. Consider the sequence of digits of pi. It can be proven that every repeating or terminating decimal corresponds to a rational number. Since pi has been proven to be irrational, its decimal expansion does not repeat or terminate.
[QUOTE=Falubii;46317904]That particular problem has already been simplified significantly. Notice that you have an (x-7) in both the numerator and denominator. These clearly cancel leaving you with only (x^2+7x+49), which you can evaluate by just plugging in the value you're taking the limit to. The trickiest part to most limit problems is really just factoring. If you end up calculating an indeterminate form such as 0/0, you need to find a way to factor out the term in the denominator that's giving you trouble.
[editline]October 2014[/editline]
what he said[/QUOTE]
...oooooh. That makes a lot more sense. Awesome, thanks.
[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]
Get rid of (x-7) at bottom, because when x = 7, (7-7) = 0, and you know you cannot divide stuff with zero.
[editline]24th October 2014[/editline]
[QUOTE=JohnnyMo1;46318708]An infinite string of numbers does not have to be repeating. Consider the sequence of digits of pi. It can be proven that every repeating or terminating decimal corresponds to a rational number. Since pi has been proven to be irrational, its decimal expansion does not repeat or terminate.[/QUOTE]
I don't know why, but irrational numbers scare me.
Just figured out, I really have big problems with writing hand calculating.. I mean, I almost always get (+) and (-) sign wrong somewhere.. I do not have problems with conceptual understanding, it is just that i am sort of dyslexic or something like this.
Any solutions?
[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 do you mean by random?
What do you mean by repeating?
What is a sequence of infinite numbers?
Starting my Statistical Methods in Applied Computer Science course in about 10 days. Apparently only 15-20 people take it each year, a few Ph.D students in the group. And you only have to pass a single assignment to get a B in the course.
Not sure if I'm supposed to be scared or not.
[QUOTE=Falubii;46317895]But there's infinite random numbers to choose from.[/QUOTE]
Meant to say sequence of digits.
[QUOTE=Swebonny;46321956]Starting my Statistical Methods in Applied Computer Science course in about 10 days. Apparently only 15-20 people take it each year, a few Ph.D students in the group. And you only have to pass a single assignment to get a B in the course.
Not sure if I'm supposed to be scared or not.[/QUOTE]
That sounds pretty scary, not gonna lie.
It also sounds like my dream class.
[QUOTE=Swebonny;46321956]Starting my Statistical Methods in Applied Computer Science course in about 10 days. Apparently only 15-20 people take it each year, a few Ph.D students in the group. And you only have to pass a single assignment to get a B in the course.
Not sure if I'm supposed to be scared or not.[/QUOTE]
Better not under-estimate class, this way (even if you know some stuff) you won't fail. But do not fear, just be smart and learn
Hey, I want to type up some maths notes for my exam, I'm allowed to take in 1 page of notes. But how can I type the symbols? Most are easy but specifically the ones with weird formatting like the square brackets on a matrix, I'm not really sure how to do those.
Is there software I can use?
[QUOTE=reevezy67;46325529]Hey, I want to type up some maths notes for my exam, I'm allowed to take in 1 page of notes. But how can I type the symbols? Most are easy but specifically the ones with weird formatting like the square brackets on a matrix, I'm not really sure how to do those.
Is there software I can use?[/QUOTE]
Read the OP.
Just finished my math subject GRE. Now I can flush all this useless shit out of my brain to make room for stuff that looks like what mathematicians actually do.
Does anyone else do anything like Decision Maths like we do here in Further Maths A-Level and if so does anyone else think that it's a fucking joke
[sp]Also holy shit this thread exists this is brilliant[/sp]
[QUOTE=JPlus;46329797]Does anyone else do anything like Decision Maths like we do here in Further Maths A-Level and if so does anyone else think that it's a fucking joke
[sp]Also holy shit this thread exists this is brilliant[/sp][/QUOTE]
Not sure if you're doing edexcel or not but D1 was a piss take. D2 is where things got interesting.
[QUOTE=agentalexandre;46329853]Not sure if you're doing edexcel or not but D1 was a piss take. D2 is where things got interesting.[/QUOTE]
Yeah I'm doing edexcel, they don't offer D2 at my school but holy shit if D1 isn't just connecting a bunch of dots and doing stuff i already did in my computing gcse
This is definitely one of the modules I'm getting 90% on for that A*
Find all the lines that pass through Q=(4,3) and have the same distance to P1=(0,0) and P2=(0,2).
Anyone? One of the questions from today's linear algebra test and I want to see if I was correct.
I'm not sure what the question is asking. "Same distance to those points?"
There's a line. It passes through a point Q. The distance from this line to each of the points P is the same.
Remember this
[IMG]http://upload.wikimedia.org/math/2/a/e/2ae89917912e4c37c8673d56ac84fa81.png[/IMG]
I'm still not sure.
[editline]28th October 2014[/editline]
Could you just give me the idea so I can sleep well?
I don't know if my method would work, but you can make a system with three unknowns, but it looks complicated even if you manage to simplify it.
I can't make something sexy but it'll end up like this:
|4a+3b+c|=|c|=|2b+c|
[QUOTE=JohanGS;46345572]Find all the lines that pass through Q=(4,3) and have the same distance to P1=(0,0) and P2=(0,2).
Anyone? One of the questions from today's linear algebra test and I want to see if I was correct.[/QUOTE]
Edit:
Do the lines have to maintain equidistant distance from [I]both[/I] points? Or just two cases, one for each point?
My intuition says all such lines must be perpendicular to the line joining P1 and P2
[video=youtube;BOx8LRyr8mU]http://www.youtube.com/watch?v=BOx8LRyr8mU[/video]
MIT Open Courseware appreciation post
[QUOTE=JohanGS;46345572]Find all the lines that pass through Q=(4,3) and have the same distance to P1=(0,0) and P2=(0,2).
Anyone? One of the questions from today's linear algebra test and I want to see if I was correct.[/QUOTE]
If I understand the question, the key point is what sort of lines have the same (shortest) distance to 2 points.
I've not come across it before, but as I can see it, there are 2 classes - those parallel to the line through the 2 points, and those passing through the point between the 2.
In this case that translates to vertical lines and those going through (0,1). So we want to know which go through Q, answer:
The vertical line is x=4
The line through (0,1) is y=x/2 + 1
You can prove this algebraically using the formula Cosa8888 gave:
[; \frac{ |ax_0 + by_0 + c|}{\sqrt{a^2+b^2}} = \frac{ |ax_1 + by_1 + c|}{\sqrt{a^2+b^2}} ;]
[; |ax_0 + by_0 + c| = |ax_1 + by_1 + c| ;]
now we either have:
[; ax_0 + by_0 + c = ax_1 + by_1 + c ;]
or
[; ax_0 + by_0 + c = -ax_1 - by_1 - c ;]
which rearranges to
[; -\frac{a}{b} = \frac{y_0 - y_1}{x_0 - x_1} ;] (i.e. the line has the same gradient as one through the 2 points)
or
[; a \frac{x_0+x_1}{2} + b \frac{y_0+y_1}{2} + c = 0 ;] (i.e. the line goes through the midpoint of the 2 points)
I'm working on some calc 1 homework and I'm a little stumped on question 6
[IMG]https://dl.dropboxusercontent.com/u/5168294/ShareX/2014/10/2014-10-28_20-45-33.png[/IMG]
my TA gave us the hint that abs(x) <= y can also be written as -y <= x <= y but when I apply that I get almost the same inequality but I have another + 1/8whatever on the right side of the inequality. am I doing something wrong? I'll take a pic of my messy work if needed
[url=https://dl.dropboxusercontent.com/u/5168294/irl%20pictures/2014-10-28%2023.11.34.jpg]my work[/url]
Square both sides (or rather all three sides) of the inequality to get rid of that ugly square root in the middle.
If you look at the latter two sides in the inequality alone you wind up, after squaring, with:
[URL]http://www.texpaste.com/n/fkgqnh47[/URL]
Which is obviously true for all a > 0.
[editline]29th October 2014[/editline]
CBF doing the other side. Watching Sherlock Holmes.
Figured it out. In an earlier question I proved that L(a + h) >= f(a + h) and applied that to the inequality
Do a laplace transform, always do a laplace transform
Fourier transform best transform
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