Complex analysis question involving maximum principle: Let f(z) = e^(2z), find the maximum of |f(z)| as z varies over the region {z ∈ C : Re(z) ≥ 0, Im(z) ≥ 0, Re(z) + Im(z) ≤ 1}
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Complex analysis question involving maximum principle:
Let f(z) = e^(2z), find the maximum of |f(z)| as z varies over the region {z ∈ C : Re(z) ≥ 0, Im(z) ≥ 0, Re(z) + Im(z) ≤ 1}
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- Consider the function X(x, y) 1 x²+y²+1* Please find equations for the following level surfaces for A, and sketch them: i. X(x, y) = } 1 ii. A(x, y) = 10 Please find k such that the level surface X(x, y) = k consists of a single point. Why is k the global maximum of X(x, y)?Hu(x , y) = 3(x^2)y-y^3 and f(0)=i , please find f(z) = u(x , y) + iv(x , y) , write f(z) in z type
- II f(x, y, z) dV for the specified function 3. f(x, y, z) = xe"-22; 0< x < 2, 0< y< 1, 05. [Local Optimization] Let f = f(x, y) = x³ + x²y — y² – 4y. (a) Find and classify all critical points of f on all of R². (b) Find and classify all critical points of f on the line y - z. (c) Find and classify all critical points of f on the curve y = 2². -For f(x, y, z) = x? – 2x + y? %3D | Then f(-1,0,-1) is local minimum f(-1,0,-1) is local maximum none f(1,0,-1) is local minimum f(-1,0,1) is local minimum f(1,0,1) is local minimum f(1,0,-1) is local maximum f(1,0,1) is local maximum f(-1,0,1) is local maximum5- fis the function defined by f (x) = x² + 2x + 2 , and (C) is the graph off. _ a) Show that f(x) = (x + 1)² +1 b) Consider the translation of axes defined by X = -1+x ;Y = 1+ y (the new origin is O'(-1,1) Determine the equation of C with respect to the new axes X'OX, Y'0'Υ . c) Draw (C). d) Deduce the table of variation of-its-elements-of-symmetry and its extremunLet / be the function defined by f(x)=- axis (a) Find the area of R B I U X² В / Y X X₂ R (2+2)² for -2Exercise 5. Consider the function f(r, y) = sin(ry), 0< < a, 0< y<1. • find local maximum and minimum if they exist • does the function f have global extremum? If it is the case find global maximum and minimum if they exist • graph the function in rz-plane, in the plane y = 1 and in the plane r = ySEE MORE QUESTIONSRecommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
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