Archives for Pure Math - Page 3
Given conditions: lim ? → ? ? ( ? ) = ? lim t→a g(t)=b lim ? → ? ? ( ? ) = ? lim x→b f(x)=c To prove: lim ? → ? ? ( ? ( ? ) ) = ? lim t→a f(g(t))=c
Given conditions: limt→ag(t)=b\lim_{t \to a} g(t) = blimt→ag(t)=b limx→bf(x)=c\lim_{x \to b} f(x) = climx→bf(x)=c To prove: limt→af(g(t))=c\lim_{t \to a} f(g(t)) = climt→af(g(t))=c Using the definition of the limit: limt→ag(t)=b\lim_{t \to…