[카이스트 방학숙제2] winter 2022 assignment 2 [더플러스수학]

Problem 1 Suppose that a function \(\displaystyle f : \mathbb{R} \rightarrow \mathbb{R}\) satisfies the following conditions for all real values \(\displaystyle x\) and \(\displaystyle y\): (i) \(\displaystyle f(x + y) = f(x) · f(y)\). (ii) \(\displaystyle f(x) = 1 + xg(x)\), where \(\displaystyle \lim\limits_{x \rightarrow 0} g(x) = 1\) Show that the derivative f′(x) exists at every value of x ..

원문링크 : [카이스트 방학숙제2] winter 2022 assignment 2 [더플러스수학]