# Search results

1. ### Theorems every mathematician should know

Let's compile a list of theorems we think every mathematician ought to know! I'll start: Stoke's Theorem: If M is a smooth n-dimensional manifold, and \omega is a compactly supported (n-1) form on M, then \int_{M} d\omega = \int_{\partial M} \omega
2. ### Has this equation got a solution?

Actually, let me clarify: Let R be the space of real numbers. R x R (pronounced "R cross R") is the set of all ordered pairs (x,y) where x and y are both in R. When you graph a function f(x) = ???, you are looking at every x and finding the unique y value that lies above it. In fact, the...
3. ### Has this equation got a solution?

This is what you are looking for: http://en.wikipedia.org/wiki/Exponentiation#Negative_nth_roots The solution is x = 1, but it depends on how you make your definitions. If you define the square root to be a relation instead of a function, you can say that sqrt(1) is both 1 and -1.
4. ### Recognize a product of two vars in Mathematica?

In your case, the simplest thing to do is replace (R*W) with some variable (say t). Then you just take Limit[x*t^2 + 4*x, t -> 0]. In your example you are only really taking a one dimensional limit, after all. If you do need to take a multidimensional limit, you say: Limit[x*(R*W)^t + 4*x...