EX: Find all residues of f(z) = Sol: there are f(z)= 50 Z 11 11 (Z+4) (Z-1)² 50 Z 32²² +42-7JZ=-4 12= Lim Z-1 200 25 dz 8 507 50 Z Z³+27²-7Z+4 -8 simple pole at Z=-4 double pole at Z=1 -Lim. Z-DI (2+4) (50)-50Z*A (2+4)² How did he get the value inside the circle
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- Find the absolute maximum and the absolute minimum of f(x,y)= 3xy-3x-6y+1 on the closed triangular region whose vertices are (0,0), (6,0), and (0,4).Determine Taylor's formula of order 1 and center a = (0, 0) of f(x)=ex1sin(x2).Determine the 1st and 2nd degree Taylor polynomials L(x,y) and Q(x,y) forf(x, y) = x √y for (x,y) near the point (1,4).
- Use field II to sketch the graphs of the solutions that satisfythe given initial conditions. a) y(0) = 1 b) y(0) = 2 c)y(0) = -1Determine the 1st and 2nd degree Taylor polynomials L(x,y) and Q(x,y) forf(x, y) = tan−1 (x + 2y) for (x,y) near the point (1,0).1. Find the natural cubic spline sN (x) passing through the 3 points (xj, yj) given by (0, 2), (2, 3), and (3, 1).Then evaluate sN (1).
- Show that the solution of initial value problem: d^2x/dt^2 + w^2x = F0cosAt, x(0)=0, x'(0)=0 is x(t)= F0(cosAt-coswt)/(w^2-A^2). b) Evaluate lim,y>w F0(cosAt-coswt)/(w^2-A^2).Assume that after months, butterflies’ populace in 1000 is calculated as: f(w)=12w+cos(16w)+n×100 Find maximum and minimum populace in 1st five months. Where n is your arid number for example if your arid number is 19-arid-1234 then n=1234(a)Assume that after w months,butterflies’populace in 1000 is calculated as: f(w)=12w+cos(16w)+n*100 Find maximum and minimum populace in 1stfive months.Where n is your arid number for example if your arid number is 19-arid-1147 then n=1147
- Let f (x, y) = 3xy − 6x − 3y + 7. Find the absolute maximum and absolute minimum values of f over the triangular region with vertices (0,0), (3,0) and (0,5).find absolute maximum and minimum of f(x,y)=x^3+3xy-3y^2+2 in a region whose vertices at (-1,-1) (-1,1) (1,1) (1,-1)Find T4(x) Taylor polynomial of degree 5 of the function f(x)=cos(x^3) at a=0