Question 12 Question 13 Use the definition f'(z0) = lim (2) - f (Zo) of the derivative to find the6.Find the image of the semi-infinite strip x20, 0s ysT under thetransformation w= e², and label the corresponding portions of the boundaries.7.Use the ɛ,8 - definition of a limit to prove the following limit.lim (az + b) = az, +b, for complex numbers a and b with a ± 0.8.Use Limit Laws to evaluate the following limits:iz -1422a) limb)lim (z2 – 4z+2+ 5i)c)lim2+0 (z – 1)?z+2+i4z° +zlim9.Prove the following limit.= 002+0 z+i10.Use the precise ɛ,8 - definition of continuity to prove that if f(z) is continuousat zo then f(z) is continuous at Zo-11.z- z0derivative of f(z) =for z +0.12.Use differentiation formulas from calculus to find f'(z).a)f(2) = 3z? – 2z+ 4ib)f(z) = (2z+5)(z+i)³az +b13.where a, b, c, d are complexFind the derivative of the function T(z) =cz +d°numbers such that ad – bc + 0. When is T'(z) = 0?14.Use the Cauchy-Riemann Equations to show that f'(z) does not exist at any point.a)f(z) = Zb)ƒ(2) = e*eiy15.Use the Cauchy-Riemann Equations to show that f(z) = z Im(z) is onlydifferentiable at z = 0 and find the value of f'(0).16.Use the Cauchy-Riemann Equations to show that f(z) = z' is differentiable forall z and find f'(z).

Name: Question 12 Question 13 Use the definition f'(z0) = lim (2) - f (Zo) o
Uploaded: 2024-03-20T07:07:50.000Z
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Description: Question 12 Question 13 Use the definition f'(z0) = lim (2) - f (Zo) of the derivative to find the6.Find the image of the semi-infinite strip x20, 0s ysT under thetransformation w= e², and label the corresponding portions of the boundaries.7.Use the