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- Sketch a graph of the function f(x) = 5 cos| 6+ 3 -87 -71 -6 -SA -47 -3T 27 -T 1 2 3n 47 57 6n 7n 8yT -2 -3 -4(1) Let f(x) = 1, x > 0 with domf= R++. Find the conjugate of function f(x).Let g be an analytic function with g(-i) # 0, g(3)(-i) = -12, and g(4)(-i) = -36. _g(z) If f(z) = (z+i)4 then Res f (z)\z=-i =
- 1. (a) Draw the graphs of the functions x and x in the plane. Then find all integers n > 2 such that (0, 0) is an inflection point of the function f(x) = x". (x + 1)®x³(x – 2)ª(x – 4)³ for all x. Find all x (b) The second derivative f" of f is given by f"(x) corresponding to inflection points of the graph of f. (c) A polynomial function g has degree 18 (like the degree of f" in part (b)). What is the maximum number of inflection points that the graph of g could possibly have? Explain your answer. (d) From (a) - (c) we see that just because g"(c) = 0 does not mean that (c, g(c)) is an inflection point. What additional property must exist for (c, g(c)) to necessarily be an inflection point?Q1) Graph the following functions: V4 - x2 ,-22. Let f(z) : D C be a complex function. Is it possible for both f(z) and f(z) to be analytic? • If Yes, give an example. • If No, explain why.Given the functions Ax) = /x+ 3 and g(x) = x' + 2x- 8, determine the domain of the combined function y = Ax) - g(x). %3D a) cannot be determined O b) {x e R, x 2-3} c) {x e R, - 4Find the function with the grandinian.3. Suppose the complex function Se, f(2) = { 0, z + 0; z = 0. (a) Where is f (z) differantiable? Prove your answer. (b) Where is f(z) analytic? Prove your answer.SEE MORE QUESTIONSRecommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
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