Exercise 3 Arc length (1 + 2 + 3 pts) The function shown here is 0.3- x cos - for x> 0 0.2- y (2) = {for x = 0 0.1 a) Calculate the derivative the function and investigate its behavior in the limit a0. b) Let s (x) be the arc length of the curve related to the point x1 0.2 0.3 -0.1- -0.2- 1 / T. Write down an integral expression -0.3- for s (x). c) Prove that s (0) = 0, i. e. the total length of the curve between r = x and x = 0 is infinite. Instead of solving the integral, the curve can be approximated by a zigzag line made up of straight sections to estimate its length. Note: The "harmonic series" E: = 1 +++ ... diverges. 3 n = 1