Answer Happy

QUESTION 12 Read the following theorem and its proof and then answer the questions which follow: Theorem. Let to functions p and be analytic at a point. If p(0) 0,q(10) 0 and gʻ(16)0, then simple pole of the quotient p/q and MI) (2) p(20) (a) Proof. Suppose p and q are as stated. Thema is a zero of order m1 of 4. According to Theceem 1 in Section 82 we then have that qiz)=(x-2)(). Furthermore, as is a simple pole of p/qand whereof) We can apply Theorem 1 from Section 50 to conclude that ResSince g(z)=(26), we obtain the desired result. D (12.1) Explain why as is a zero of order m=1ofq (12.2) What properties does have? (12.3) How do we know that is is a simple pole of p/7 (12.4) Show that g) — 4²(²a). (2) (2) (3)