Multivariable Definition and 524 Threads

Hi, I was reading ratemyprofessor.com (i know - not a good thing, as most bad reviews are written by lazy students) and I came across something a bit strange. Somebody said that he wouldn't recommend taking the first semester of calculus-based physics unless you've taken calc 3 (multivariable)...

Hey, I'm a high school student (11th grade) and I'm working on a computer algebra system for a research project. Most things are are going well (sums, products, derivatives, integrals, series, expansion, complex analysis, factoring basic expressions, etc.). However, I am having difficulty...

lim (sqrt(|x|)y) / (x^2+y^2) (x,y) -> (0,0) so I've substituted y = x, y = sqrt(|x|) as well as the substitutions for polar coordinates. the function seems to approach infinite which means that the limit does not exist. the problem asks to show whether the limit exists or not and then to prove...

Just curious how to define continuity for mult dim. functions. I know that the topological and set theorectical definitions work in a very abstract setting; but I just don't know how to prove (for example) that f(x,y) = x + y or f(t,z) = t*z is continuous, other than saying something like: Well...

For integrating over type 1 and type 2 regions, why does the g(x) or g(y) bound have to be the inner integral? Thanks!

Multivariable Calc Image-Graph Problem! Homework Statement Given a function f: R-R2 , by f(t) = (t, t^2 - cos(t)), which represents a curve in the xy plane parametrically, give a function whose GRAPH represents this same curve. 2) Also, give a function h whose level set for height k=0...

Hello all. So I am trying to integrate a function of this form: \int\intF(x,y)\delta[a(Cos[x]-1)+b(Cos[y]+1)]dxdy The limits of integration for x and y are both [0,2Pi). I know that this integral is only nonzero for x=0, y=Pi. So this should really only sample one point of F(x,y)...

Homework Statement lim (x,y)→(3,1) | (x2y - 6xy - x2 + 6x - 9y - 9) / ( (x-3)4 + (y-1)2 ) Homework Equations none The Attempt at a Solution Since we have the indeterminate form '0/0' when we simply substitute (x, y) = (3, 1) we need to show the limit Does Not Exist. we will show...

Homework Statement Find the local maximum and minimum values and saddle point(s) of the function. f(x,y) = 1 + 2xy - x^2 - y^2 Homework Equations The Second Derivative Test: let D = D(a,b) = fxx(a,b)*fyy(a,b) - [fxy(a,b)]^2 if D > 0 and fxx(a,b) > 0, then f(a,b) is a local minimum...

Homework Statement The equation z(e^(xy)) + z^5 + y = 4 implicitly defines z as a function z = f(x,y) near (0,2,1) (a) find df/dx and df/duy where x = 0, y = 0, and z = 1 (b) find the maximum rate of change of f at the point (0,2) Homework Equations sorry, my first post here not sure what i...

Hello everyone, I'm new to this forums. Been lurking around for a while, but finally decided to join :) So anyways, I'm a current high school senior right now, taking Calc BC. I'm hoping to major in a math-related field (mathematics, physics, or electrical engineering) when I get to college...

Homework Statement Prove that (\frac{\partial u}{\partial x})^{2} + (\frac{\partial u}{\partial t})^{2} = e^{-2s}[(\frac{\partial u}{\partial s})^{2} + (\frac{\partial u}{\partial t})^{2}].Homework Equations u = f(x,y) x = e^{s}cost y = e^{s}sint The Attempt at a Solution I started out by...

I have uploaded my question along with all of my work to Google Docs as a PDF, it can be found https://docs.google.com/fileview?id=0B35_M3cbY5nxMTE5Y2NjMzgtYzQ0MC00YmNjLTg1ZDktZmVlYjA4MTQxNzE2&hl=en&authkey=CL-llawP", which is why I did not follow the template provided. (I already had it in a...

Homework Statement Let x=x^2ysin(u)tan(v), where x(u,v) and y(u,v) are smooth functions that, when evaluated at u=1 and v=-3 satisfy x=2.112, y=4.797, \partialx/\partialu = -3.491, \partialx/\partialv = -2.230 , \partialy/\partialu = 1.787 , \partialy/\partialv = 1.554. Then the...

Homework Statement http://img195.imageshack.us/img195/8196/mathqshwk4.jpg Find https://webwork.elearning.ubc.ca/webwork2_files/tmp/equations/f3/d5a53499bbf12cafa144440e3095781.png and [PLAIN]https://webwork.elearning.ubc.ca/webwork2_files/tmp/equations/b1/ce11cb4b480b6159791b1605b6f2681.png...

Estimating Maximum Error, Odd Question? (Please Help Today!) Homework Statement Suppose that T is to be found from the formula T = x(e^y + e^-y), where x and y are found to be 2 and ln(2) with maximum possible errors of |dx| = 0.1 and |dy| = 0.02. Estimate the maximum possible error in the...

Homework Statement Find that the limit exists, or show that the limit does not exist. lim (x,y) --> (0,0) of (x^2 * sin^2y)/(x^2 + 2y^2) Homework Equations ?? The Attempt at a Solution i used the lines x=0 y=0 and both times got the limit 0 so i attempted to prove the limit...

I have an function with 4 variables. Each of the 5 variables are bounded between to real numbers. Is there an easy way to find a maximum value of the function? Here is the equation: http://yfrog.com/jleqnp I have MathCAD and Mathematica software available to me. I'm not very familliar with...

Hello!I am a student in class 10 at the moment and am eager to do 11 physics but a devilish problem exists...calculus!Could anyone of you suggest me which topics to complete in maths before approaching calculus.Also suggest a few good books to experience calculus.pls!

Homework Statement When you substitute polar coordinates into a multivariable limit, do you treat theda as a constant when evaluating? (I know how to use polar coordinates to evaluate a limit but haven't learned what they are yet) Homework Equations The Attempt at a Solution

Homework Statement A given surface contains all points G such that the distance from G to the plane z=4 is double the distance from point G to the pt. (2, -3, 1). Find eqn for the surface. Homework Equations I thought the distance formula for a point to a plane would help, but I can tell...

Homework Statement Find the equation of the sphere centered at (-7,6,7) with radius 2. Normalize your equations so that the coefficient of x^2 is 1. Homework Equations (x-xo)^2 + (y-yo)^2 + (z-zo)^2=r The Attempt at a Solution (x-(-7))^2 + (y-6)^2 + (z-7)^2 = 2 it saids to...

Homework Statement Find the scalar and vector projection of the vector b=(3,5,3) onto the vector a=(0,1,-5) . Homework Equations The Attempt at a Solution What I've tried is multiplying all the i's and j's and k's together and adding up everything because you get a scalar...

Homework Statement Find the Equation of the sphere with points P such that the distance from P to A is twice the distance from P to B. A(-2, 4, 2), B(4, 3, -1) Homework Equations The equation of a sphere would probably be the most relevant equation. That is (x-h)^2 +...

if Cost(r)=0.01(2\pir2+v/\pir2(2\pir))+0.015(4\pir+v/\pir2) v=hpir2 how does one show for the optimal radius/height for any volume i.e. where the cost will be the minimum for that volume? all my attempts have ended with 0=0 help please? i'll give you cookehz ^^

Hello all, I am currently studying multivariable calculus, and I am interested in the Taylor series for two variable function. I am not sure where to begin; I cannot understand any of the proofs (which are apparently sparse) on the internet; they all just state it using a sigma sum; not...

Well, I have a week and a half until my first classes in my first year of college. My math class is multivariable calculus. However, while I aced Calculus in high school, I'm worried that college-level may be of a different caliber. So, I wanted to ask what should I know walking into that...

Homework Statement Find the surface area of the ellipsoid (x/a)^2 + (y/a)^2 + (z/b)^2 = 1. Homework Equations If G(u,v) is a map from R2 to R3 that parametrizes the surface, then the area of the surface is equal to the double integral over the domain of G of the norm of the cross...

this fall I am taking differential equations at my university without having taken multivariable calculus part 2 (my school splits multivariable calc into 2 quarters, I've only taken the first quarter). I have taken linear algebra (took it last quarter) so basically what I'm wondering is will...

Hello. I was wondering if I should self study multivariable calculus or introduction to proofs? I am an entering high school senior (contrary to what my username might suggest), and I just took a Calc 2 class last spring. I can only do one or the other, and I don't know which one would be...

For a single variable we have \int_{x_1}^{x_2} f(x) dx = F(x_2)-F(x_1) if f(x) = dF/dx. f(x) is then a total derivative. What is the analog in 3D so that \int_V f(\vec{x}) d^3x does not depend on the values of f in the interior of V? In case there is not a single answer...

Right, high school student here, I may want a book on multivariable/vector calculus soon and I was wondering if you have any suggestions.. I like the look of https://www.amazon.com/dp/0130414085/?tag=pfamazon01-20 but regrettably it seems to expensive for me.. Bear in mind that I live in...

Homework Statement Consider that f(x, y) = [sin^2(x − y)] / [|x| + |y|]. Using this, prove: lim(x,y)→(0,0) f(x, y) = 0 Homework Equations Definition of a limit, etc. The Attempt at a Solution I don't know how to start... I've been trying to self-teach limits for a while and...

hi i want to find values of a,b,c such that.. Minimize (a+b+c) constrained to (x-a)^2 + (y-b)^2 + (z-c)^2 less than equal to R(z) (x-a)^2 + (y-b)^2 + (z-c)^2 greater than equal to r(z) can anyone help me solving this?? which method should b used for better computation??

Homework Statement Is the function f(x,y) defined by f(x,y) = (yx^3 - 3y^3)/(x^2 + y^2), (x,y)!=(0,0) =0, (x,y)=(0,0) continuous everywhere in R^2? Give reasons for your answer. Homework Equations The Attempt at a Solution I changed f(x,y) into polar coordinates and found the limit as...

Homework Statement We say that a differentiable function f : \mathbb{R}^n \rightarrow \mathbb{R} is homogenous of degree p if, for every \mathbf{x} \in \mathbb{R}^n and every a>0, f(a\mathbf{x}) = a^pf(\mathbf{x}). Show that, if f is homogenous, then \mathbf{x} \cdot \nabla f(\mathbf{x}) = p...

A hall charges $30 per person for a sports banquet. For every group of over 50, the hall will decrease the price by $10 per person, in excess of 50 people. a. Write revenue as a multivariable function of the number of people, q, in excess of 50 and the price per person, p. b.Write a...

Homework Statement If T is implicitly defined via the relationship f(x, y, z, T) = 0 to be a differentiable function of x, y and z, show that the first partial derivative of T with respect to z can be found using: \frac{\partial T}{\partial z} = -\frac{\partial f}{\partial z} / \frac{\partial...

Homework Statement Find limit as (r, θ)----> (0, pi/2) for the function: r= (w secθ)/(secθ+tanθ)^(Vs/Vr) Both w and Vs/Vr are constants in this question The Attempt at a Solution I tried with L'hopital but it didnt turn well as when I differentiate secθ, I got ln (secθ + tan...

Find the volume of the solid in the first octant of xyz space, bounded below by the coordinate axes and the unit circle and bounded about by z = 8xy A) 1/2 B) 1 C) 2 D) 4 E) 8 I know we need a double integral. The bound below should be the unit circle which would be x^2 + y^2 = 1. So...

can we define a multivariable power series (laurent series) \sum_{i,j,k,l,...=-\infty}^{\infty}a_{i,j,k,l,...}(X-a)^{i}(Y-b)^{j}(Z-c)^{k}(W-k)^{l}... indices i,j k and l run over ALL the integers positive and negatives how could i calculate the coefficients ?? a_{i,j,k,l} ?

Homework Statement 1. Verify the given moments of inertia and find the center of mass. Assume each lamina has a density of p=1. The problem gives a circle with a radius a. 2. Find the area of the surface of the portion of the sphere x^2 + y^2 + z^2 = 25 inside the cylinder x^2 + y^2 = 9...

Homework Statement I don't need to state the whole problem; it's the definitions at the beginning that are giving me trouble. Homework Equations So it says, Definition: A function f(x,y) is continuous at a point (x0,y0) if f(x,y) is defined at (x0,y0), and if lim(x,y)-->(x0,y0)...

Homework Statement F(x,y)= sin(x)sin(y)sin(x+y) over the square 0\underline{}<x\underline{}<pi and 0\underline{}<y\underline{}<pi (The values for x and y should be from 0 to pi INCLUSIVE) Homework Equations The Attempt at a Solution I know I need to do the partial derivatives...

Homework Statement Prove the following, using the meaning of a limit: Homework Equations epsilon > 0, delta > 0 0 < sqrt(x^2 + y^2) < delta | f(x) - 0 | < epsilon (1) The Attempt at a Solution So, I know that I have to elaborate on the inequality in (1), further. However, I'm...

Homework Statement Evaluate this limit, lim (x,y) > (0,0) f(x,y) where f(x,y) = ((8x+8)(2x+3y)^2) / (sqrt(3x^2 + 14xy + y^2) - sqrt(x^2 -2xy + 8y^2)) Homework Equations No? The Attempt at a Solution I figure the first attempt is to rationalize this fraction. But after I...

Hello there, I'm currently enrolled in Calculus II (Integral Calculus), and I am slowly working my way through Spivak's Calculus. I intend to take Multivariable Calculus next semester. The course description is as follows: I was wondering if there were any clearly recommended books...

Homework Statement Define f(0,0)=0 and f(x,y) = x2 +y2-2x2y-4x6y2/(x4+y2)2. Show for all (x,y) that 4x4y2<=(x4+y2)2 and conclude that f is continuous. Homework Equations The Attempt at a Solution Showing the inequality is trivial, but I do not see how I can conclude the...

Defining differentiability for multivariable functions we want not only for the partial derivatives to exist but also local linearity. Because my question is the same also for the single variable case, I'll pose it with a single variable function. In one variable we have that local...

I have a question about university course offerings. This semester I'm taking a course called "Introduction to Analysis," which uses Edward Gaughan's Introduction to Analysis, and is basically just a more rigorous/proof-based coverage of the topics we learned in the first two semesters of...