[고려대 미적분학 기출] 2018년 2학기 미적분학1 -exam1

1. Using the precise definition of limit, show that \(\displaystyle \lim\limits_{x \rightarrow 1}\frac{x^2 +1}{x^3 +x}=1\). (12pts) 2.

If \(\displaystyle f(x)\) and \(\displaystyle g(x)\) are differentiable functions such that \(\displaystyle f \left( g(x)\right)=\tan x\) and \(\displaystyle f'(x)=1+f^2 (x)\), \(\displaystyle \left ( -\frac{\pi}{2}...