Recent content by stratusfactio

The question asks to find an integral that gives the specified volume below the cone z=r, above the xy-plane, and inside the sphere x^2 + y^2+z^2 = 8. So essentially, we're finding the volume inside the cone? I know that the very top of the cone would include the top of the sphere...

Homework Statement F=<xy, x-y> and C is the triangle joining (1,0), (0,1) and (-1,0) in the clockwise direction. Homework Equations How do I have the second part of this curve? The Attempt at a Solution Apparently, there should only be a sum of two integrals. So I got that curve...

Homework Statement Evaluate the triple integral of the region E, where E is the solid w/i the cylinder x^2+y^2=1, above the plane z=0, and below the cone z^2=x^2+y^2. So is the plane z=0 same as the xy-plane? I was doing a homework problem that has Homework Equations I just need...

Homework Statement Set up the triple integral for the region bounded by: x=y^2, z=0, x+z=1Homework Equations The Attempt at a Solution y= ±sqrt(x); z=0 & z=x+1 I'm just lost on how to find the x integral. I know the dz integral goes from z=0 to z=x+1, and I know the dy integral goes from...

Homework Statement Just a general question for studying purposes. How do you find a vector parallel to a plane? Let's say that we have a plane 2x-3y-z=0...I know that the perpendicular vector to this plane is <2,-3,-1> but how do I use this information to determine a parallel vector?

Homework Statement Find a vector parallel to the line of intersection of the planes given by the equations 2x-3y+5z=2 and 4x+y-3z=7. Homework Equations How do I go about this? I know we have two vectors <2,3,5> and <4,1,-3> but where do I go from here? The Attempt at a Solution...

Homework Statement A cone C, with height I and radius I, has its base in the xz-plane and its vertex on the positive y-axis. Find a function g(x, y, z) such that C is part of the level surface g(x, y, z) = 0. Homework Equations What would be the formula for the cone such that the base of the...

Homework Statement Give a formula for a function whose graph is described. Sketch it using a computer or a calculator. A cone of circular cross-section opening downward and with its vertex at the origin.Homework Equations I know how to draw the cone and the properties of a cone, so that's not...

Let me clean that up for you: d^2x_1+2x_1=x_2 d^2x_2+2x_2=x_1

So I'm self teaching myself Multivariable Calculus from UCBerkeley's Youtube series and an online textbook. I'm up to Stokes Theorem and I'm getting conflicting definitions. UCBerkeley Youtube series says that Stokes Theorem is defined by: \int {(Curl f)} {ds} And then the textbook says that...

Ahhh, I see. Is that because the diagonal of the triangle is the line 4-y?

Homework Statement **The book I'm working from doesn't have solutions for even numbered problems and the two problems I'm about to show you guys are even, so if you guys don't mind, I would just like to know if I have the right concept, or if I messed up anywhere. I wouldn't have a way of...

^Haha. I'm self teaching myself Multivariable Calculus using this online book: http://www.mecmath.net/calc3book.pdf in conjuction with Youtube's UCBerkely Multivariable Calc lectures. It's just weird because I did all the steps and analyzed each step and can't see where I went wrong...we may...

Homework Statement calculate the integral f · dr for the given vector field f(x, y) and curve C: f(x, y) = (x^2 + y^2) i; C : x = 2 + cos t, y = sin t, 0 ≤ t ≤ 2π (2pi) Homework Equations Would the vector F simply be <(x^2+y^2),0> since there is no j component? The solution is 4pi...

I don't think you could use the quad. formula here because it's not in the form of ax^2+bx+c. Did you go over division? I believe you have to use long division to find the zeroes.