Multivariable Definition and 536 Threads

I was presented with the two following questions: \lim_{\substack{x\rightarrow 0\\y\rightarrow 0}} \sin\frac{xy}{xy} and \lim_{\substack{x\rightarrow 0\\y\rightarrow 0}} \sin(\frac{xyz}{xyz}) I figured I would do a simple substitution: let t = xy for the first one, and the limit becomes as t...

Ok, i think i understand this one, but it's giving me a bit of trouble in terms of comprehension, so I thought I'd get some help on it. I need to find and sketch the domain for: f(x,y)= \frac{x^2 + y^3}{x^2 + y^2 -1} The way i see it, that would only be undefined when the denominator...

R is the interior of the region, in the x,y plane, bounded by the parabola y = 4 - (x - 3)^2 and for which x \leq 3\,\mbox{and}\,y \geq 0. Sketch the region R, and evaluate the double integral \iint_R 2xy\,dx\,dy I've drawn the region, but I am unsure as to what to do with the integral and how...

A rectangular box is to have a volume of 96m^3. The 4 sides and the top are to be made of a material of density 1kg/m^2 and the flat base is to have a density of 2kg/m^2. Suppose that the base is of size x meters by y meters. It was found in the first question that the mass, M in kg of the box...

At my school multivariable calculus (aka calculus 3) isn't required under the computer science corriculum. I'll have to take other math courses but we're not forced to take calculus 3 and as far as I know it is not a prerequisite to any computer science course my school offers. The subject seems...

I got this question as a take home exam question, and I can't figure it out for the life of me: The temperature T(x,y,z) throughout a region in space is given by: T(x,y,z) = 3*x^2*y*2+z^2 An insect is confined to move on the surface S : x^2 + y^2 = z. The insect is at the point...

I need to compute the partials of z with respect to x and y of: xy + z + 3xz^5 = 4 at (1,0). I already showed that the equation is solvable for z as a function of (x,y) near (1,0,1) with the special implicit function theorem, but that's the easy part. Could someone explain to me how to begin...

I need to "write the number 120 as a sum of three numbers so that the sum of the products taken two at a time is a maximum." I think this means that x+y+z=120 and xy+xz+yz=maximum. Can someone help me begin this problem?

For f(x,y) = x^2 + y^2 + 3xy I need to find the critical points and prove whether or not they are local minima, maxima or saddle points. I thought the only critical point was (0,0) since Df = (2x + 3y, 2y + 3x) = 0. Doesn't this make (0,0) a local min? The reason I doubt this now is because upon...

Hi, I'm having trouble with the following question. I would like some help with it. Q. A function f:A \subset R^n \to R^m is continuous if and only if its component functions f_1 ,...,f_m :A \to R are continuous. Firstly, is there a difference between C \subset D and C \subseteq D? Anyway...

Here is the problem I'm having some trouble with. The answer is fairly simple, it is the power of the e function. (the parabola x = y^2 + 1) I'm not sure how to get that, i could use some hints/help, thanks!

Just wondering if anyone can prove these to me: lim (x,y)->(a,b) f(x) * g(y) = lim x->a f(x) * lim y->b g(x) (As well as the n dimensional case) Also, why when you try to show that a limit doesn't exist you can keep a variable constant, or do something like y=x, or approach from some...

I can't figure out how to do this problem. Any help would be appreciated. Given that the curve C is defined by x=t^2-4, y=t^3+1,z=5te^(t^3+1), write an equation (in rectangular form and with integral coefficients and constants) for the normal plane to C at P (-3,0,-5). Edit: Here's what I've...

I need to find the limit as x,y->0 of (x^2+y^2)(ln(x^2+2y^2)) anylitically. since the limit of this is 0(-infinity) which is indeterminant .. I tried to approach it along the line y=x which gives: lim(x->0) of [2x^2*ln(3x^2)]. Again, that gives 0(-infinity). Now, I haven't done calculus in 6...

Hello, I was wondering if anyone can help me with this problem. Show that the line with equation 2ax+2by=a^2+b^2 is tangent to the circle with equation 4x^2+4y^2=a^2+b^2 If this is true, wouldn't the derivative of the circle equation be equal to the first equation? Would I just take...

lim of cos((x^2 + y^2) - 1)/(x^2 + y^2) as (x,y) approaches (0,0) I have no clue how to tackle this problem. I tried to find the level set so at least I can have a clue of what the graph looks like, but then, I didn't know how to find the level sets either. If I set c = the equation, I...

Please let me know if I derived this correctly (I did it a while back, and can't find the notebook): v(x,y)=u(r(x,y),s(x,y)) (derivations) At some point I come across this: \frac{\partial}{\partial x} \frac{\partial u}{\partial r} which I wrote as \frac{\partial^2 u}{\partial...

Next week in my multivariable class, we'll be starting curvature, and, nerd that I am, I looked ahead to learn it ahead of time. I can usually at least understand the basics of a new concpet by myself, but curvature really threw me off. Maybe my brain's not right for it, maybe the book sucks...

Do any of you know of excellent advanced multivariable calculus textbooks? If so please list them. (Don't mention James Stewart) Thanks

i need some suggestions on books on multivariable calculus. preferably not too expensive.

Hey can you guys check my answer. Question: Use the Divergence Theorem to calculate the Flux of the vector field F(x,y,z)=xi + y^2j - zk through the unit sphere centered at the origin with the outward orientation Solution: div(F) = 1 + 2y - 1 = 2y Flux = \int_{W} div(F) dV = \int_{0}^{1}...

Let S be the surface given by the equation 9x^2 + y^2 − z^2 − 2y + 2z = 1, Show that the straight line r(t) = <1, 1, 1> + t<1, 0, 0> is normal to the surface S at the points of intersection. I set both equations equal to each other and I found their points of intersection are (1/3,1,1) and...

hello, i was wanting to teach myself multivariable calculus. i am currently in calculus BC AP. that class isn't challenging enough for me. do any of you out there know any good sites or good books for multivariable calculus. any help would be greatly apprecaited. thanks in advance.

I'm confronted with the following question that may of may not have a solution: You are given eight variables, A, B, C, D, E, F, G, and H. These variables are integers. You know that: A/B > E/F and C/D > G/H Is it possible that (A+C)/(B+D) < (E+G)/(F+H)? I've tried...

I am reading a book on multivariable calculus for my course and I have tried the question : \int_{0}^{\frac{\pi}{4}} dx \int_{0}^{Sec(x)} y^3 dy apparently the answer is 1/3..I have TRIED to get this answer... yet i cannot yield 1/3...help! (anyone from the UK...I have a good A...

Hi to all, Anyone knows sites or got online books that would help a student like me learn all about multivariable functions & their geometric visualization, 2 and 3 diminsional graphs, derivatives, integrals, and more explination?

I have a huge test tomorrow and I forgot to bring home my textbook... could anybody direct me to a site with lots if info on Calculus 3? Thanks.

Can someone explain how to separate a multivariable differential equation into two independent differential equations? I'm having an issue solving for the potential in spherical co-ordinates in terms of r and theta.

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)...

I was wondering, if it wouldn't be too boring for any of you, if someone could post an intro to multivariable calculus, from partial differentiation up through the grad, curl, divergence of vector fields, preferably with applications to physics. Maybe you can post a sticky or something. I'm...

Hey everyone, our teacher assigned us 15 pretty tough problems to finish by the end of the year and my partner and I have gotten through all but these last two, which none of the other teachers at school can figure out either. Any help would be greatly appreciated, thanks! In the (Epsilon ...

Multivariable calculus problem involving surface area I am not sure where to start with this problem...Any help I receive would be greatly appreciated: Compute the surface area of the portion of the cone x^2 + y^2 = z^2 which lies between the planes z=0 and x + 2z = 3.

Determine an equation of a plane that intersects the plane x+y+z=3 at an angle of 60 degrees.

OK OK I know Double Integral is from Multivar Calculus, I was just wondering what we use it for... I heard is good for volumes, but can't yhou also find volumes by just 1 integral? And also, aside from integrals in Multivar calc, what else are useful? I want to get a intro to it, can...

Hi, I had problem solving one question. Please help me. I included my answers. Please check to make sure that my way is right. 1. IF f(x,y) = x^2 +4y^2, find the gradient vector f(2,1) and use it to find the tanenet line to the level curve f(x,y) = 8 in the xy-plane at the point (2,1)...

Hey, I need your help doing some of math problems. Q) A particle's position at time t is determined by the equation of the helix r(t) = < cost, sint, t> Let P be a point with a coordinates (0,1,pie/2). 1. Find the curvature k(t) at any time t. 2. Find...