I'm having a little trouble trying to figure out these problems. Any help would be appreciated. g(x) = (x^2 - a^2)/(x-a) when x≠a but 8 when x=a... how do i find the constant a so that the function will be continuous on the entire real line? f(x)= x^3 - x^2 + x - 2 on closed interval [0,3] f(c)=4. How do I find the value of c that is guaranteed by the Intermediate Value Theorem? ---I've proven via IVT that there exists a 0 in [0,3] but I do not know how to find the c value. if f(x)=g(x) for x≠c and f(c)≠g(c) then either f or g is not continuous at c. True or False. --- I haven't a clue. I can't even think of an example where f(x)=g(x) but f(c)≠g(c). this last one I just want to make sure i'm doing it right. Show that the Dirichlet function f(x)= 0 if x is rational and 1 if x is irrational is not continous at any real number. if I just write D(x) = lim m→∞ lim n→∞ cos^2n (m! pi x) is that showing that the function is not continuous at any real number? Again, I'd appreciate any help or pointers in the right direction. Thanks.