1. (30Pts) Calculate an estimate for the Euler's number, e, to 6 significant figures using the Maclaurin series expansion of e*. 2. (70Pts) Trajectory of a thrown ball is defined by (x, y) coordinates can be modelled with the equation: 14 y 12 10 y=tan (6)x- g x + yo 8 2v cos (0) g: acceleration of gravity 6 4 2 0 10 20 20 30 40 50 50 The ball leaves the hand of the thrower at y = 1.5m with initial velocity vo 30 m/s. If the trower wants to hit an object at x=50 m distance and y=10 m elevation, calculate the required value of the throwing angle 6, with an error tolerance &s=0.005% by using the bisection method, the false-position method, the Newton-Raphson method and the secant method. Present your results in tables for bracketing methods: Iteration XI Xu Xr a (%) 1 2 Xi a (%) and for open methods: i 0 1 Note: - - Writing program codes for the solution of problems is highly recommended (You can use any programming language of your choice). You can't use built in functions for the solution of HW questions. You need to either write program codes (advised) or do calculations by hand (not advised, will take a lot of time and effort). There is no third option. Present your results in a HW report. If you wrote program codes you need to add them to your submission. If you calculated by hand use at least 5 significant figures in calculations. Always use radians for trigonometric functions.