Multivariable calculus Definition and 277 Threads

Homework Statement Maximize the Riemann Sum ##\Sigma^{n}_{i=1}x_{i}*y_i## subject to constraints ##\Sigma^{n}_{i=1}x^{2}_{i}=1## and ##\Sigma^{n}_{i=1}y^{2}_{i}=1 ## Homework Equations My teacher doesn't speak English very well. I'm in Calculus 3 and the average on his exams are...

Homework Statement Sketch the following curves on separate number planes. y= 2x^2 x^2 + 2y^2= 4 Homework Equations The Attempt at a Solution For the first one, would the intersection of the curve with the y-axis be at y=2 ( I have attached a diagram of my solution). The...

[Question] Hi, my teacher gave us this problem, and he couldn't figure out why method was incorrect and why I got the answer I did. Given we know the gradient slope = <-56,1.886> at the point (2,0) on a surface f(x,y), in what direction, expressed as a unit vector, is f increasing most...

Note: <= means less than or equal to, >= means greater than or equal to 1) Prove formally that lim xy^2 / (x^2 + y^2) = 0 (x,y)->(0,0) without breaking the vectors into components. Let X=(x,y). We want to prove that for all epsilon>0, there exists a delta>0 such that if...

1) lim [x(y^2)] / (x^2 + y^2) (x,y)->(0,0) Find the value of the given limit, if it exists. Using polar coordinates, set x = r cos(theta), y = r sin(theta) Then, the given limit = lim [r cos(theta) r^2 sin^2(theta)] / r^2 r->0 = lim r [cos(theta)...

hey everybody, I'm currently using the book Multivariable Calculus by james stewart 6E and i have to say... it SUCKS. SUCKS just like his single variable calculus book that we are forced to by at university. So I really need a good book, which one would you guys recommend?

need sites for solved problem pls... anyone know a website that has solved problems for complex numbers (multivariable calculus)? my finals is on Monday and there aren't enough sample problems in our book, some are very basic.. i really need help..

Find the equation of reflection of the sphere in (x-1)^2+(y+2)^2+(z-4)^2=16 with respect to the point (2,1,-2). There was another question asking for the reflection equation but it was with respect to the xy-plane so it just meant changing some signs. What I came up with for this question was...

Homework Statement The height of a hill is given as the following: h \left( x,y \right) =40\, (\left( 4+{x}^{2}+3\,{y}^{2} \right) ^{-1}) There's a stream passes the point (1,1,5) which is on the surface of h. The stream follows the steepest descent. Find the equation of the stream...

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 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...

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...

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...

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.

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 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...

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.

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...

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...

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...