Define f : R" → [0, 0) by letting f(x) = (1 – ||æ||<)*72 if ||x|| < 1 and f(x) = ( if ||x|| > 1. Prove that f is continuous on R™. (To prove that f is continuous at a given xo E R", consider separately the following three cases: ||xo|| > 1, ||xo|| < 1, ||x0|| = 1.)

et △ABC be a triangle in S^2 (the two-dimensional sphere). Let the dual point C'∈S^2 of C be defined by the following three conditions:(i) d(C' , A)=π/2(ii) d(C' , B)=π/2(iii) d(C' , C)≤π/2A' and B' are defined analogously. Thus we get a dual triangle △A' B' C'. More precisely, △ABC is a non-degenerate triangle, andit follows (you may assume) that △A' B' C' is too.(question) Are there triangles △ABC in S^2 identical to their own dual △A'B'C'?   I would be very thankful if you could provide some explanation with the steps, thank you in advance.