Recent content by brunette15

Hey everyone, I am trying to evaluate the following integral: \int z(z+1)cosh(1/z) dz with a C of |z| = 1. Can someone please guide me with how to start? I have tried to parametrise the integral in terms of t so that z(t) = e^it however the algebra doesn't seem to work...

Hi again I like Serena :) I am aware that we could do that but for this particular case i am trying to prove the divergence theorem of Gauss :/

I am given the sphere V= x^2 + y^2 + z^2 =< 1 I have converted it to spherical coordinates: x = rsin(t)cos(f) y = rsin(t)cos(f) z = rcos(t) where t ranges from 0 to pi, and f ranges from 0 to 2pi. I am unsure how to go about this problem from here. Any guidance would be really appreciated :)

I am trying to evaluate \int\int xy dxdy over the region R that is defined by r=sin(2theta), from 0<theta<pi/2. I am struggling on where to begin with this. I have tried converting to polar coordinates but am not really getting anywhere. Any guidance would be really appreciated (Crying)

Thankyou so much! I know how to figure it out from here :D

I am give the following curve r(t) = (t+1,0.5(1-t),0) where t ranges from -1 to 1. I am now trying to derive a new parametric representation of this line segment using the arc length as the parametric variable. I have integrated r'(t) from -1 to 1 and found that the length of the segment ranges...

I see! Thankyou! :D

That helps a lot! Thankyou so much! :D

I am trying to find the field lines of the 3D vector function F(x, y, z) = yi − xj +k. I began by finding dx/dt =y, dy/dt = -x, dz/dt = 1. From here I computed dy/dx = -x/y, and hence y^2 + x^2 = c. For dz/dt = 1, I found that z = t + C, where C is a constant. I am unsure where to go from...

My question regards finding the field lines of the 3D vector function F(x,y,z) = yzi + zxj + xyk. I was able to compute them to be at the curves x^2 - y^2 = C and x^2 -z^2 = D, where C and D are constants. From my understanding the field lines will occur at the intersection of these two...

Thankyou so much :)

I am trying to sketch isotherms of the field cos(x)sinh(y). I am not sure how to begin with this. Can someone please help/hint me through what i have to do?

Thankyou so much!

Thankyou so much I was able to figure it out from there :)

I am trying to find an equation for a plane that passes through the point (2, 1, 5) however is also perpendicular to the line that passes through the points A(0, 1, 1) and B(1,-1,-1). I am unsure how to begin with this. I have started by finding the normal vector to A and B = (0,1,-1), to find...