Last edited by Paradoxica; 19 Mar 2017 at 10:17 PM.
If I am a conic section, then my e = ∞
Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.
Last edited by InteGrand; 19 Mar 2017 at 10:48 PM.
Oh damn, looks like the brute way is the only way out of that one. Was hoping for a shortcut
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I got asked a question but I haven't seen the notation before
What is that isolated nabla supposed to mean?
Nabla phi I am sure you understand, that is the gradient of phi and is a vector-valued function. Which can be regarded as a triple of functions (f,g,h) from R^3 to R.
Nabla cross (f,g,h) denotes the curl of the vector-valued function (f,g,h).
If you write Nabla as (d/dx,d/dy,d/dz), then Nabla x (f,g,h) is defined the same way as the usual cross product between two 3-d vectors. (Just the first "vector" consists of a triple of differential operators, whilst the second consists of a triple of real-valued functions on R^3. So instead of multiplying real numbers (vector components) together as in the defn of the usual cross product, we are applying differential operators to functions.)
eg first component is dh/dy-dg/dz.
Last edited by seanieg89; 25 Mar 2017 at 10:57 AM.
(The notation Nabla dot (f,g,h) is the divergence of a vector field and is understood in the same way.)
If you keep cheating you won't learn. Why are marks so important?
Seriously? If I am stuck on a question why can I not ask for help? Accusing me of cheating on an assignment if I genuinely can't do my homework is just low.
So for a continuous mapping f: are the following always true
(I didn't really define the domain and codomain of f so just assume whatever's convenient please)
1) U is closed => f^-1(U) is closed
2) U is open => f^-1(U) is open
3) U is closed => f(U) is closed
4) U is open = f(U) is open
5) U is compact => f(U) is compact
6) U is path-connected => f(U) is path connected
Don't really need proof, just yes/no is sufficient
There was a question in my test that I could not do and I'm seeking a solution please
Yeah it is a boundary point. Here's some hints of a possible method. Note that S is just the graph of y = f(x) := sin(1/x) (x =/= 0). Use (or show) the fact that f attains the value 1 for arbitrarily small values of x > 0 to deduce that (0, 1) is a boundary point of S (noting that any ball around (0, 1) contains points not in S also, as there will be points in it with y-value greater than 1).
Last edited by InteGrand; 7 Apr 2017 at 3:39 PM.
I get lost in this Einstein summation convention so can I see how this problem would be approached using it?
Last edited by leehuan; 25 Apr 2017 at 8:21 PM.
Even with the diagram in front of me I still struggle to figure out my boundaries of integration.
Last edited by leehuan; 30 Apr 2017 at 9:12 PM.
I think spherical is preferred here (could be mistaken). But using the best approach, how would you determine the limits for this
It might be easier to use cylindrical coordinates. The way rho varies is different depending on what range phi is in. When phi is such that your point in the region lies within the "ice cream cone" part of the region, then rho will vary from 0 to a. For phi larger than the angle make by the cone to the vertical, rho will vary from 0 to the value of rho at the point on the sphere x^2 + y^2 + (z-a)^2 = a^2 with this phi value. You can find these using the relations between Cartesian and Spherical Coordinates.
I might be misinterpreting the question but I thought that they're basically asking for 1/4 * area of curve of intersection, which happens to be an ellipse through (0,0,8) passing through (0,8,4) and (8,0,4).
If I'm right, how do I use surface integrals to get to the answer of ? And if I'm wrong, how do I get back on the right path?
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