Dear math expert, kindly help to provide working solution for the questions. Thank you

All questions carry the same marks. Answer ALL questions. 1. A steel pipe is being carried down a hallway that is 3 m wide. At the end of the hall there is a right-angled turn into a narrower hallway, 2 m wide. What is the length of the longest pipe that can be carried horizontally around the corner. 2 m 3 m 2. Let f (x) = 1+ -. Use the definition of deivatives to show that x 1 f' (x) = -- 2x2 \\ + 1 3. Express the following as a definite integral So f (x) dx and find its exact value. 1 lim E n-+00 i= 1 Vnvn ti 1