Question

If lim (x->a) [f(x)g(x)] then the lim is f(a)g(a).
Would this be true?

If f'(a) exists, then lim (x->a) f(x) = f(a)
Would this be false?

Answer 1

1) consider \(f(x)=x-a\) and \(g(x)=\frac{1}{x-a}\)

2) differentiability implies continuity