In this problem we outline a different derivation of Eulers formula.(a) Show that y1(t) = cost and y2(t) = sin t are a fundamental set of solutions ofy+ y = 0; that is, show that they are solutions and that their Wronskian is not zero.(b) Show (formally) that y = eit is also a solution of y+ y = 0. Therefore,eit = c1 cost + c2 sin t (i)for some constants c1 and c2. Why is this so?(c) Set t = 0 in Eq. (i) to show that c1 = 1.(d) Assuming that Eq. (14) is true, differentiate Eq. (i) and then set t = 0 to conclude thatc2 = i. Use the values of c1 and c2 in Eq. (i) to arrive at Eulers formula.
Lecture 16: Rates of Change & Higher Derivatives (Sections 3.4 & 3.5) Recall the following: Average Rate of Change y = f(x) x1 2 Instantaneous Rate of Change