Calc 3 Definition and 104 Threads

Homework Statement 1)show that the lines l1 and l2 intersect and find their point of intersection. l1: x+1=4t y-3=t z-1=0 L2: x+13=12t y-1=6t z-2=3t 2)The plane through the points p1(-2,1,4),p2(1,0,3) that is perpendicular to the plane 4x-y+3z=2 3)Find the distance between the given skew...

I mostly just want to know if I did this correctly... And if not, where I went wrong. Homework Statement Of \overline{U}=(-2, 6) is the vector \overline{AB} and the midpoint of the line segment from A to B has the coordinates (2,1). Find A and B. Let \overline{A}=(a1, a2) \overline{B}=(b1...

Homework Statement Let vector 'v'=<1,-1,5> and vector 'w'=<40,-19,-1>. Represent 'w' in the form of 'w'='g'+'h', where 'g' is parallel to 'v', and 'h' is orthogonal to 'v'. This is related to the dot product. But I don't know where to begin Homework Equations 'v' is a vector. 'g'...

two questions. I know I'm doing the work right, but I can't get my answers to match and they are pretty close. I think it's just some arithmetic errors. Help? I've been trying to solve my mistakes forever. I can't find them! Homework Statement Use the parametric equation of an ellipse x =...

Calc 3 exam tomorrow! Check my solutions please! Takeing a practice exam but don't have the solutions, anyone who could verify my solutions would be appriciated! First problem Find the scalar equation of the plane that passes through (2,-1,0) and is perpendicular to the line x=1-t...

Homework Statement I know that x+y+z=0 is a tangent plate to my sphere at (0,0,0). I want to find the tangent plane for my sphere at (1,-2,3).Homework Equations Suppose that his is my sphere (x-a)^2+(y-b)^2+(z-c)^2=R^2 (a,b,c) is the center of my sphere while R is the radius of it. The Attempt...

Homework Statement I got a quiz back today, and i disagree with a lot of the things that my professor graded, but this one really made me upset. (direct link, some can't see http://forum.bodybuilding.com/attachment.php?attachmentid=3329041&d=1304709473) Homework EquationsWhat happened there...

Homework Statement r=(1-x)(1+x) Find and classify all of the critical points Homework Equations D=fxx-fyy-(fxfy)^2 (can't read my notes to well or find it on the internet) The Attempt at a Solution r=-x^+1 f'= -2X f"=-2 Because -2<0 There is a maximum(1), I don't know the...

2. If y(t) is the vertical distance traveled at time t, then the same reasoning as used in Problem 1shows that v2= (2gy)/(1+I*) at any time. Use this result to show that y satisfies the differential equation dy/dt=sqrt(2g/(1+I*))*(sin alpha)*sqrt(y) where a is the angle of inclination of...

Hi I wanted to take calc 3 this summer and i want to start brushing up as I took calc 2 back in spring 08. I was wondering if there are infinite series in a typical calc 3 course? If so I need to brush up on them. Also concerning the laundry list of different integration techniques for the...

Need help in finding Limits of Integration! :) (Calc 3) Homework Statement Evaluate Integral: f * n dS, where "f" and "n" are vectors and "*" is DOT PRODUCT. Where, where (a) f = (x2, ey, 1), S: x + y + z = 1, x ≥ 0, y ≥ 0, z ≥ Homework Equations ummm none The...

Hi guys, Do you think it's a good idea/possible to take Physics 2, Differential Equations, Linear Algebra, and Multivariable Calculus together in one semester?

What calc 3 topics will I need to learn before taking ODE? I'm going to be taking both at the same time and I want to know if there is stuff I need to be familiar with before starting. The class is using Fund of Differential Equations & BVP by Nagle (5th ed) and I have no syllabus yet.

Homework Statement Find a vector that has the same direction as the given vector but has length 6. ‹4, 2, -2› Homework Equations L = ((x-i)^2+(y-j)^2+(z-k)^2)^.5 The Attempt at a Solution For some reason I am just stuck. I don't know how to start. I assume L =...

Here's where I try to explain Stokes' theorem in my own words and you tell me if I'm right / what I need to clarify on. Essentially, it's a method to compute a line integral around a closed curve in three dimensions, with a given vector field F, without having to parametrize this field and...

Use cylindrical coordinates to evaluate the triple integral , sqrt(x^2+y^2) where the region integrated is the solid bounded by the circular paraboloid z=9-16(x^2+y^2) and the xy-plane. I'm having trouble deciding what the bounds for r would be.

Homework Statement Find dy/dx ; sqrt(xy) = 1 + yx^2 or 0 = 1 + yx^2 - sqrt(xy) Definition : dy/dx = - F_x / F_y; A = F_x = 2xy - 1/2 (xy)^-0.5 * y B = F_y = x^2 - 1/2(xy)^-0.5 * x Then dy/dx = -A / B But the answer according to the book, is this : 4(xy)^-1.5 - y...

Homework Statement In the xy plane, where distances are measured in feet, a 96 lb object is moving from left to right on the curve y=e^-x. At t-0 its speed is 6ft/s and is speeding up at (square root of 8) ft/s^2. what is the total force on it at that point? Give floating point values for...

Homework Statement a. the derivative of a vector function is obtained by differentiating each component function b. if r(t) is a differentiable vector function, then d/dt the magnitude of r(t) = the magnitude of r'(t) c. the binormal vector is B(t) =N(t)xT(t) d. if k(t)=0 for all t, the...

Homework Statement reparametrize the curve r(t)=e^t*i+e^t*sin(t)*j+e^t*cost*k with respect to arc length measured from the point (1,0,1)in the direction of increasing t Homework Equations arc length= integral( r'(t) from a to b) The Attempt at a Solution i don't know how to start...

[b]1. Homework Statement I am suppose to use polar coordinate data to find derivatives, ie x = r cos(theta) y = r sin(theta) r^2 = x^2 + y^2 [b]2. Homework Equations show dtheta/dy = cos(theta)/r show dtheta/dx = -sin(theta)/r...

Can anyone give me some suggestions of some essentials, calc or non-calc, that I should review and be comfortable with in calc 3? I know trig sub is supposedly important, and I'm assuming other basic derivative/integration techniques will be coming up a lot too...a lot of topics are bound...

I took calc 2 6 months ago... and I am just wondering which parts of calc 1,2 i should review for both diff eqns and calc 3. should i also review linear algebra? which parts? (ie: eigenvectors, eigenspaces, row reduction)? also what content is heavy in diff eqns and/or calc 3? should i review...

Homework Statement This is from Larson's Calculus Early Transcendentals 4th Ed (Pg. 786) A 600-pound boat sits on a ramp imclined at 30 degrees, as shown in Figure 11.32. What force is required to keep the boat from rolling down the ramp? Homework Equations The solution gives the...

The region in question is bounded by: the cylinder (x^2)+(y^2)=(R^2) the parabola x = y-((y^2)/R) the planes z = H, y = 0, and z = 0 and the velocity field is: F = yz(i)+xz(j)+xy(k) and we need to calculate the outward flux of the field of the region at z = H (the top of the...

I really do apologize if this is in the wrong place. A long story short, At my school Calc 3 is a 4 creidt course with a lab and I really don't have room to fit it in my schedule next semester. But I can fit in Elementary Diff Eq. My question would be is it better to take a (much) harder...

Hi, this is a calc 3 question. I know the binormal is given by B = T x N where Binormal vector, B Tangent vector, T Normal vector, N Also, B = (R'(t) x R''(t)) / | R'(t) x R''(t) | T = R'(t) / | R'(t) | Does that mean N = R''(t) / |R''(t)|?

Hello, Thank you very much for takign the time to help me out. This is an applied calculus 3 (multivariable calc) level problem. I have an answer, but it is nonsensical as the units are not in accordance with units of charge, C. Homework Statement Instructions: Use Gauss' Law for...

Anyone know an online school/program that offers this?

can you somehow factor the following equation ? sqrt(9sin^2(t)+16cos^2(t)+1/4)

Homework Statement Using the triangle inequality show that for all vectors a, b, c in R^n: ||a-b|| <= ||a - c || + ||c - b || (a, b, c are vectors) Homework EquationsThe triangle inequality states: ||a+b|| <= ||a|| + ||b|| The Attempt at a SolutionIm really not sure what to...

Hello ya'll, new to these forums but I've been reading around and enjoyed what I've read. Wanted to get some feedback about some classes coming up this semester. I'm a Sr. high school student, and will taking one class at the HS (AP Bio), and 4 at a college nearby. I took AP Calc BC and...

Homework Statement i needed to find the max and min possible volume for a box with edges that = 200cm and surface area that = 1500cm^2 using Lagrange multipliers.Homework Equations edges: 4x + 4y + 4z = 200cm Area: 2xy + 2xz + 2yz = 1500 cm^2 Volume = xyzThe Attempt at a Solution i brought it...

This is a problem I got from a Stanford class in calc 3: Let f(x,y,z)=xyz+3. Find an equation of the level surface that passes through the point (1,-2,0). This is as far as I have gotten: The constant for the level surface will be k = xyz + 3 = (1)(-2)(0) + 3 = 3. The equation is thus 3...

I want to start by saying that I know this may be perceived as a "stupid" question, but I'm quite curious... What class more difficult...Calc 3 or DE? I'm into my final week of Calc 3, and next week I start DE. I decided to take both during summer sessions as I did this for Calc 1-2 last...

I'm a senior in High School, and took BC Calculus as a Junior and this last semester a 1-semester Calc 1&2 honors class, mainly for those those who took AB in High School at the University of Utah. (It's surprising how bad you can do on the AP test and still get a 5). I'm signed up for the next...

Hi, I was wondering if there is a bank of test of questions (and answers) available on the internet. I do all my assigned homework and more but I find that the questions on the tests require a lot more insight than the assigned problems or most of the problems in the textbook. I figure it...

hopefully this is the right place to ask this. But do you think I would be able to handle calculus 3 (multivariable) without taking (formally) calculus 2? I'm going to be a high school senior next year, and I've taken a class in calc 1. I've self studied the material in calc 2 and it doesn't...

Hi how do I go about finding out what N is to 3 x √27 = 3^N this can be written as 3 x (√3 x √3 x √3) which makes 9√3 = 3^N now where though i presume n must be a fraction somthing like x/2 ? x is a number? Is this right. How do i go about finding the answer?

Hello everyone, I'm having issues figuring out how you find the bounds of each of these graphs, I have the solution manual but I still don't see how they did it. For example: The directions say to evaluate the double integral:http://img241.imageshack.us/img241/903/scan0001nx8.jpg On the...

Hello everyone. Awhile ago I took honors calc 3, but only the 2 credit course, not the 4 becuase computer engineering didn't require the 4 credits. But now that I switched to computer science I have to take the 2nd half of calc 3 but I don't remember hardly anything. This is the description...

Homework Statement F(x,y,z) = (x^2y^3z)i +(sin(xyz))j +(x^2yz)k S is the part of the cone y^2=x^2+z^2 that lies between the planes y = 0 and y = 3, oriented in the direction of the postive y-axis My question deals with orientation (see below sec 3) Homework Equations \int_c F dr =...

Homework Statement Find the work done by the force field F(x,y) = x*sin(y) i-hat + y j-hat on a particle that moves along the parabola y = x^2 from (-1,1) to (2,4). 2. The attempt at a solution Please see attached file. The answer I get seems really, really, complicated and I have a...

Homework Statement Find the work done by the force field F(x,y) = (x+2y^2)j as an object moves once counterclockwise about the circle (x-2^2+y^2=1 by first evaluating the integral directly then use Green's Theorem and evaluate the double integral. Homework Equations W = F*D*cos(theta)...

heres is one problem i did, i photo'd it so i wouldn't have to worry about it... Am I doing it right? any problems can you see :-/ on like the 8th/9th line, I don't think I can do what I did... http://img130.imageshack.us/img130/1332/test076ze.jpg Sooo

eval. double integal sprt(1+x^2+y^2)ds S is helicoid and r(u,v) = ucos(v)i+usin(v)j+vk, with 0 <=u<=4 and 0<=v<=4pi help please i don't know what a helicoid is!

1) Rewrite the following expression in polar coordinates: (second derivative of z with respect to x) + (second derivative of z with respect to y) where x=rcos(theta) y = rsin(theta) i had first derivative of z with respect to x = (dz/dx)(dx/dr) + (dz/dx)(dx/d(theta)) same concept for...

The question asks: Find the directional derivative of f (x, y, z) = z ln (x/y) at (1, 1, 2) toward the point (2, 2, 1). What I did was find the distance between the two points to be the directional vector (i+j-k) and then I took the norm of the direction vector. so my unit vector =...

calc 3 easy question! I am trying to find the partial derivative of the following function with respect to y. I know how to find it without using the definition...but i want to know how to do it both ways. any help?? g(x,y)=x^2*e^-y I got: lim as h approaches h...

Hello guys I am not sure if I am doing this right. If you could offer any advice or point out my mistakes I would appreciate it. Problem: Sketch the graph of the domain of f(x,y,z) = \frac{1}{x^2+y^2-z} Domain: (x,y,z) \in R^3 \mid x^2+y^2 does not equal z Graph: I set f(x,y,z) = 1 and...