g: R->R
g(x) = 2 if x not equals 1
g(x) = 0 if x equals 1
f(x) = x +1 for R
"Verifiy" (sorry my english) that lim x-> 0 (gof)(x) is not equal lim x->0 (gof)(0)
If there is a contradiction with the continuity theorem of composite function, give a justification why.
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Firs part:
lim x->0 (gof)(x) = lim x->0 g(x+1) = g(1) = 2
lim x->0(gof)(0) = g(0+1) lim x->0 g(1) = 0
??
and now what is continuity theorem of composite function?