Calc iii Definition and 80 Threads

hey guys, i need some advice as to which math class to enroll in. i just got accepted to college and will be starting first semester of freshman year in september. i will be a math major, and i am really comfortable with math. So right now, i am in ap calc BC and i am confident that i can get...

Hey guys, I'm studying for a test in calc 3 tomorrow and have run into a problem. On the practice test we have a problem "Find the length of the curve: r=theta^2, 0≤theta≤pi/2" I know the length of a curve in polar coordinates is int(sqrt(r^2 + (dr/dtheta)^2))dtheta...but when I get to where...

Consider the intersection of the sphere (x-3)^2+(y+2)^2+(z-1)^2=13 with the plane x+y=0 a) This intersection should be a familiar curve. Describe the curve. b) Substituing x=-y or y=-x into the equation of the sphere does not give this curve. Explain the difference. I know that the...

Homework Statement A gun if fired with an angle of elevation of 30 degrees. What is the muzzle speed if the maximum height of the shell is 500 m? Homework Equations The Attempt at a Solution I haven't gotten very far at all. I'm not sure how to even start this one. I know that...

Not sure about the forum, sorry. Are series expands featured prominently in vector calculus?

Homework Statement A horizontal clothesline is tied between 2 poles, 12 meters apart. When a mass of 2 kilograms is tied to the middle of the clothesline, it sags a distance of 5 meters. What is the magnitude of the tension on the ends of the clothesline? Homework Equations F=mg...

Homework Statement Plane passes through points (a,b,c) and (e,f,g) parallel to x-axis Find the equation of plane Ax+By+Cz+D=0 General question for this--(a,b,c) and (e,f,g) can be any points in space Homework Equations Below The Attempt at a Solution First, I find the vector...

Homework Statement Take any plane ax+by=cz=d (any numbers should work if subsituted) Find a normal vector to the plane Read my question below Homework Equations The Attempt at a Solution I know the normal vector would be <a,b,c>. But, could a correct answer also be a scalar...

Homework Statement Show that the vector field given is conservative and find its potential function. F(x, y, z)= (6x^2+4z^3)i +(4x^3y+4e^3z)j + (12xz^2+12ye^3z)k. Homework Equations The Attempt at a Solution When I take partial derivative with respect of y for...

Hey, I am going to take either one or the other over the summer. Do you think taking LA first will help in multivariate calc?

Given vertices of regular tetrahedron OABC, prove that vector OA + OB + OC is perpendicular to plane ABC... I've been racking my brain on this one, can't figure it out... would appreciate some help I thought I'd center it on the origin: (0, 0, 0) (1, 0, 0) (0, 1, 0) (0, 0, 1) A + B...

Homework Statement "For this project we locate a trash dumpster in order to study its shape and constuction. We then attempt to determine the dimensions of a container of similar design that minimize construction cost." 1. (Already located, measured, and descibed a dumpster found). 2...

I'm confused about whether or not I'm thinking about this correctly: If I'm given an equation eg. 3x^2-2xy=3z+1 (just a random eg.) Is it a correct assumption to think of the x,y and z in the equation as corresponding to x,y and z as I'd think of them on the cartesian plane...They're...

So I have some free time this summer and was wondering if it would help to review topics from Several Variable Calculus (I believe its called calc III in most places?) before taking the class. I haven't taken calc with a lot of integrals in a year now because my freshman year in college i took a...

Homework Statement Hi there, Two points on the sphere S of radius 1 have spherical coordinates P: \phi = 0.35 \pi, \theta = 0.8 \pi and Q: \phi = 0.7 \pi, \theta = 0.75 \pi. Find a vector parallel to the line of intersection of the tangent planes to S at the points P and Q. 2. The...

Homework Statement Use vectors to find the points of trisection of the line segment with endpoints (1,2) and (7,5). Homework Equations Not sure. The Attempt at a Solution I don't really know where to start. i tried to create a standard vector equation but its a line segment not a...

I'm teaching myself calculus III off of various websites including wikipedia. However, I don't know exactly where to begin. I've started by looking at the partial derivative and parts of vector calculus. My calculus learning so far has been: Calc I: Limits Basic and complicated...

Hello everyone, i have the following problem I'm confused about! Can anyone guide me to what I'm suppose to do? I tried the following but it was wrong, he then told me I can just apply the theorem to |r'(u)| insteed of the stuff under the square root which would be more difficult. This is...

Hello everyone I'm stuck on this problem its an integral but i don't know how to integrate the log_2 part, i converted it to natural log: Here is what I have: http://img278.imageshack.us/img278/1158/integral9lo.jpg Thanks.

Hello everyone! I have a worksheet and it says Graph the following limits: (i) r(t) = <t,-t,t^2>; (ii) r(t) = <t,sin t, cos t> can that be transformed into a unit vector? like r(t) = ti - tj + t^2k? & r(t) = ti + sin (t) j + cos(t)k I'm confused on what he wants!

Hello everyone. I'm stuck on the last part of this problem. It says, Draw two distinct nonzero postion vectors a = <x1,y1> and b = <x2,y2> such that the angle between them is less than pi/2. Draw the line L perpendicular with the line determined by the bector a such that l passes through the...

Hello everyone I have a few problems I ran into doing my homework. Its on vectors. Any help would be great! The professor didn't give me any ones i could check in the back of the book and his office hours are very bad for me, sorry for all the questions! This one is probably really simple...

Hello everyone, I'm trying to figure out this point on the sphere. The orginal equation is this: x^2 + y^2 + z^2 ≤ 16; 2 ≤ y ≤ 4; Here is the picture: http://img133.imageshack.us/img133/5527/point1eo.jpg If you look where it shows a picture of the sphere and i have an arrow...

Hello everyone, I'm stuck on some problems, This is the first homeowrk assignment and I'm pretty lost! I'm going to list the directions and show you what I have done so far, any help would be great! Here is my work to the problems: //http://img175.imageshack.us/img175/4090/4108rz.jpg...

Hello everyone, I'm having some troubles figuring this out. I'm supppose to Describe the set of points whose coordinates satisfy the given equations and inequalitites. Sketch the graph. x^2 + y^2 + z^2 ≤ 16, 2 ≤ y ≤ 4; I forgot the rules of inequalitites, I see its an equation of a...

Hello everyone, it was the first day of calc III class and this one problem says: Describe the set of points whose coordinates satisfy the given equation and inequalitites. Sketch the graphs. x^2 + y^2 + z^2 = 25; x = 3; What exactly am I suppose to do? The book doesn't show any...

Hello everyone. I'm suppose to imagine the cartesian product or three-dimensional rectangular coordinate system (R^3 = {(x,y,z)|x,y,z R}) that the orgin is a source of gravity and a tight rope connects the point (10,0,0) to the point (10,0,0) to the point (0,10,0) on the tight rope holding...

Hello everyone. I'm suppose to imagine the cartesian product or three-dimensional rectangular coordinate system (R^3 = {(x,y,z)|x,y,z R}) that the orgin is a source of gravity and a tight rope connects the point (10,0,0) to the point (10,0,0) to the point (0,10,0) on the tight rope holding...

From what I can remember, this wasn't covered in my class, however it was a bonus question on a test, and I was wondering if someone could take the time to enlighten me on this one. Find \frac{\delta f }{ \delta x} and \frac{\delta f }{ \delta y} when f(x,y) = \int _x ^{x^3y} \sin (t^2) dt

I am considering taking 1 or the other and possibly both next semester. Is there any advantage to taking one of them first, will taking calc III help me with diff eq or vice versa?