44 4. Write the function f(x)=2+ ANALYTIC FUNCTIONS 1 (z = 0) Z. in the form f(z) = u(r, 0) + iv(r, 0). Ans. f(z) = = (1 + ² ) cos+ir i ( r — 1 ) sin 0. r CHAP. 2
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- Let f = -2x² + 5y² where x = cos(t) and y = sin(t). af using the chain rule. Write your answer as a function of t. Ət Calculate af Ət = Choose File No file chosen > Next QuestionQ4 A function y = f(t) is defined and continuous for all real numbers t on the closed interval [-2.5, 6.5]. The first derivative, y'= f'(t) is sketched below. For each question, give a short and brief explanation. -2 -1 2 -1+ -2+ y 1 2 3 f'(t) 4 (a) At what value(s) of t does the function f has critical point(s)? (b) On what open interval(s), the function f is decreasing. (c) At what t value(s) does the function f has local minimum point(s)? (d) On what open interval does the graph of f concave down on? (e) At what t values does the graph of f has inflection point(s)? 5 6Find the harmonic conjugate of the function and find the analytic function of f(z)=u+iv as a function of z only.