7. Suppose f and g are entire functions and convenience, let p= all z, |f(2)| < 5|g(2)|, this implies that f and g have the same zeros. suppose the has finitely many zeros. For min{|z; – zk| : 9(2;) = g(2k) = 0, z; 2k}. Suppose further that, for a. Show that the only singularities of h =1 are the removable ones at the zeros of g. (Hint: you know something about h in a neighborhood of a zero of g.) b. Prove that there is a constant c, c < 5 so that f(z) = cg(2) for all z. (Hint: use Part a. and an important theorem, applied to an entire function that is usually equal to h.)

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.