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hint: write f(1) - f(0) as a telescoping sum.

no one even wants to try?

Let n be a positive integer and suppose f is continuous on [0,1] and f(0) = f(1). Prove that the graph of f has a horizontal chord of length 1/n. In other words, prove there exists x \in [0,(n - 1)/n] such that f(x+1/n) = f(x)

ok, that's what i thought after working with the problem for a bit. so is the answer "b" because you get a function of y?

8. Let f : R^3 → R a function all whose first order partial derivatives are continuous and such that f(0, 1, 1) = 0, f_x(0, 1, 1) = 1, f_y(0, 1, 1) = 2, f_z(0, 1, 1) = 3. Find lim t-->0 f(t2, cosh t, et) f(t, cos t, cosh t) 9. Let f : R2 → R such that f(x, y) = f(y,−x) for all (x, y) ∈ R2, and...

So I'm taking a freshan analysis class. I've never covered converting things to binary and other number systems before, and in a chapter about sequences the book mentions binary and has an exercise to convert the square root of two to six decimal places. Can someone tell me what binary is and to...

so can anyone help me prove this? I'm trying to teach myself induction...

yes, sorry, i meant for the case when the polynomials has the same leading coefficient as the variable approaches infinity.

Sligtly more complex than the average one, I'd assume. How would I go about proving that the limit of of a rational expression consisting of two polynomials of the same degree goes to one and the limit of one where the degree of the bottom is greater than the degree of the top goes to zero. I'd...

proof: if n is rational and m is irrational set n + m = l is rational then l + (-n) = m is rational, a contradiction

yes? no? just let me preemptively thank you all for all the help you've given me thusfar and for all the help you might choose to give me in the future. you guys rock!

how does i<0 relate to a_i. like a_i seems to me to be just a constant, with the _i part just differenting it from other as. when they say that i<0 do they mean that a_i <0? and am i correct in saying that all of the elements of F are (a_-nx^-n,...,a_0x^0,a_1x,a_2x^2,...,a_nx^n)? and the as...

to reiterate: i honestly have no clue where to start and I'm not even sure i understand the problem correctly. to give you a clue as to where the class is mathematically: it's a class for people who might want to be math majors (or minors), so pretty much everyone in it is a freshman in one...

Do you think you could break the problem down into less formal language for me? That might help me get anywhere!

I have absolutely no clue how to start here. Let F be the set of expressions of the form a = sum from i in Z of a-sub-i*x*i, where each a-sub-i is an element of R and {i < 0 : a-sub-i does not equal 0) is finite. (X is a formal symbol, not a number). An element a belonging to F is positive if...

I'm an Orthodox Jew and I'm *very* skeptical of the Bible Codes. And besides, there are far more explicit predictions the Bible and the Talmud have made. The Talmud (together with a Rabbi from about 200 years ago), for examples, predicted Germany's chain of events (including its military setuo)...

4xyzw<=x^4+y^4+z^4+w^4 (((( w=(xyz)^(1/3) )))) 4(xyz)^(4/3)=x^4+y^4+z^4+(xyz)^(4/3) 3(xyz)^(4/3)=x^4+y^4+z^4 ((((a,b,c=x^4,y^4,z^4 respetively)))) 3(abc)^(1/3)<= a + b + c and now use a,b,c = j^3,k^3,l^3

i got it, will post proof tomorrow.

argh i meant using a^4 + b^4 + c^4 + d^4 = 4abcd and d=(abc)^(1/3) prove a^3 + b^3 + c^3 + d^3 = 3abc for positive numbers a,b,c

I meant prove a^3+b^3+c^3>=3abc using w=(xyz)^(1/3) and yes i did mean earlier >=

i realize i might have posted this in the wrong place. I'm sorry. please move it, although i do think that it is a nice topic for this section.

So I've been thinking about this for a while for an analysis class. I proved that a^4 + b^4 + c^4 + d^4 = 4abcd. Now I'm supposed to prove the inequality above using w=(abc)^1/3/. I'm not asking anyone to do my homework for me, but maybe someone could point me in the right direction? Nice to...

I definitely picked the wrong name for this forum! But thanks! At what level or mathematics does one encounter tensors?

Anton was a great calc book. Vis a vis that infentissimal stuff: It isn't that different from what you'd normally learn. In fact, the difference is trivial. However, for a beginning calc student, do a search for "calc tutorial" and I'm sure you'll find stuff.

Can there be absolute truth without an omniscient creator? My guess is no.

For your calculus purposes (and perhaps for all purposes) infinity is just a shorthand way of picking arbitrarily large values for, say, x.

Here is my proof that 0! equals one. By _definition_ of factorial (regardless for what we chose of n) we have: n*(n-1)(n-2)(n-3)...1=n! This is equal to n*(n-1)*(n-1-1)(n-1-1-1)...1=n! However, this is also equal to n*[(n-1)!]=n! thus 1!=1*(0!) thus 1=1*(0!) thus (0!)=1 Dare I say...

I have two questions. A) Show the parallelipided with fixed surface area and maximum volume is a cube. I've already proven that we can narrow down the proof to a box. So, basically, I'm really lost on how do prove that a cube is the box with a fixed surface area and maximum volume. B)...

Math "Newb" Wants to know what a Tensor is Hey, I'll be entering my senior year of High School next year and this summer I'm taking Multivariable Calculus at UCLA. In September I'll start AP Stats. Anyway, what is a Tensor? I've always wondered this question. From what I've gathered, It's a...

Tomorrow is my first physics midterm for college. I got a 5 on the AP Physics B test, but I've never taken physics in college yet. There's hardly any calculus, so its basically AP Physics B. Does anyone know where to get sample midterms or can anyone give me some challenging practise problems...

And I use the cross of the two vectors along with one of the endpoints of the vector to get the equation of the plane, eh? Thanks e( , you are very helpful. Thanks a lot, bro.

Ok, let me be more clear: How would I find the equation of a plane parallel to a line and a point not on that line? And How would I find the equation of the plane that two vectors are on?

Thanks, guys! That answered one of them. The next questions are: "how would I find the equation of a plane parallel to a line? with one other known point" My guess is to find two points on the line, and then using the three points find the equation of the plane. "how would I go about...

Ahh ok. I thought about it a little, and that makes sense. Like if my planes were X + Y + Z = 0 and 2X + Y + Z = 0 I'd set Z equal to zero, and then I'd get a zyztem of equations and the point I'd use would be (X,Y,0, right? That makes sense, thanks gza! Anyway, do you have any answers to...

This is my post that I posted in the calculus discussion area, but I know that there are a few people here in the same class (and using the same book!) so it's probably beneficial to post it here too. edit: go me! of course I forget to post the link lol...

This is in my multivariable course. How would I find the equation of the line where two planes meet? I worked out how to find the equation of a plane perpendicular to that line going through a point, Z, (in two planes, Ax + By + Cz +D = 0 and Ex + Fy + Gz + H = 0, take the cross product of...

Me too. Vector Calculus by Marsden and Tromba, right? The T.A said that it made things overly complex and didn't explain things enough. Alas, this is what our teacher uses =p A pretty awesome introduction to calculus book, and it's also pretty definitive is Calculus by Anton. He later...

We'd never to be able to see photons orbiting something unless we stood in their orbit (or unless photons escaped).

Vectors are incredibly powerful. I've taken 4 classes of multivarient calc so far, and my knowledge of math increased exponentially!

Ok, I get it. If a points downleft and b points downright, then c is b-a . Is this correct sir? Btw, thanks for your help akg and cook!

Scuse me akg! It should have been Coordinate Planes =p mb But, wouldn't c = a - b if a points upright and b points downright?

Figured it out! If z=0, then you have the XY plane. So, find what T value makes z zero (2 in this case). Then, plug in 2 for t in x and y (you get 9 and 23 respectively). Thus, the point it intersects the XY plane is (9,23,0). That feels good!

I think I figured out my second question (!). http://envision3d.org/members/Josh/proof.GIF I don't kow how rigorous it is though ... The first one is still tearing me a new one, though!

How would I find the points of intersection of the line x= 3+2t , y= 7+8t , z=-2+t , that is, l(t) = (3+2t,7+8t,-2+t) with the coordinate plane? Also, how would I prove using vectors that the line segment joining the mdpoints of two sides of a triangle is parallel to and has half the length...

My parents are South African! Moot nee kuk prat nee sienkey and uhh, buya lekka (that's all I know, lol). chan kuk in de milles I know that too. And I also know all of N'kosi sikalel iAfrica

http://envision3d.org/members/Josh/i%20like%20spoons.jpg http://envision3d.org/members/Josh/i%20have%20a%20blue%20tie.JPG I'm the guy =p These are ~~ a year old I'm 17 now

http://envision3d.org/members/Josh/i%20like%20spoons.jpg http://envision3d.org/members/Josh/i%20have%20a%20blue%20tie.JPG I'm the guy =p edit: P.S I'm (kinda) new too! =p

Exactly what I was going to say. Just complete the square with variables.

I was wondering the same thing about taking the logarithm or ln of a function.

Because you might know one of coefficients better than the others, and depending on whereit is (inside or outsode of the radical) it's error will be less. For example, let's just say you have f(C)=2C and g(C)=(C)^(1/2) If your value of C is off by 0.5, then in f your answer will be off by 1...