I. Foundations/Comprehension (No technology allowed, show all work!) 1. Given a 1st order differential equation, Euler's method will provide an overestimate when the solution curve is concave (3 points). 2. Compute the exact sum of the following infinite series (5 points): 13 + 12 WIN n(n + 1) n=1 3. The following sequence is convergent. Find the limit (5 points). ay = cos(2 ) + 2 arctan(N) - sin (onN-7 12N+5.4. Suppose you are given the following 1st order differential equation: dy + 2xy = y dx a) Using separation of variables, find the general solution to this equation, written in the form y = f(x) (5 points). b) Besides the result of the previous part (a family of solutions), another solution not part of the family is y = _ (3 points). c) Find the specific solution (part of the family) which satisfies the initial condition y (0) = 5 (4 points)