[카이스트 미적분기출] 2008 Midterm Exam of Calculus I [더플러스수학]

1. Let \(\displaystyle f(x) = 2x + cos x \).

(a) (8 points) Verify that \(\displaystyle f\) has an inverse. (b) (8 points) Find \(\displaystyle (f ^{−1} ) ( \pi)\). 2. (15 points) Let \(\displaystyle f(x) = \sqrt{4x+1}\).

Use the formal \(\displaystyle \epsilon-\delta\) definition of limit with given \(\displaystyle \epsilon =1\) to explain that \(\displaystyle f \) is continuous at \(\displayst.....