Written assignment 3, due on Mar 7th Please make sure to provide good reasoning to all steps of your work. Full sentences are expected. A train is traveling along its track. The train's maximum speed is 40 meters per second. At the start (time 0 s ), its position is 0 m , its instantaneous speed is \(10\mathrm{~m}/\mathrm{s}\) and its instantaneous acceleration is \(5\mathrm{~m}/\mathrm{s}^{2}\)(a) Determine the degree 2 Maclaurin approximation of the train's position as a function of time Hint: The speed is the derivative of the position, the acceleration is the second derivative of the position (b) Use the approximation from (a) to get the train's approximate position after 2 seconds. Please calculate the numerical result. (c) What does the Mean Value Theorem tell you about the train's maximal possible position after 30 seconds and why? (d) Find the limit \[\lim _{x ightarrow \infty}\left(1+\frac{4}{x} ight)^{x}\](this is unrelated to the previous exercises).