2. Suppose /() = 1. Write / in the form () = u(,y) + tv(x,y), where z = 1+ ty and u and v are real-valued functions. 3.

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2 Suppose 1 Write In The Form U Y Tv X Y Where Z 1 Ty And U And V Are Real Valued Functions 3 1 (33.35 KiB) Viewed 27 times

2. Suppose /() = 1. Write / in the form () = u(,y) + tv(x,y), where z = 1+ ty and u and v are real-valued functions. 3. Let /() = 87 (A) Calculate lim(e) using properties of limits. (b) Use the e- definition of continuity to show that is continuous at: i. 4. Calculate limousing properties of limits. 5. Use the definition of a derivative (soep.65,56) to show that / (+) = 2: for all : € C, if(3) = 3+ 1. 6. Let (:) 2: (A) Use the Cauchy-Riemann equations to determine where g is differentiable. (1) Is g analytic anywhere? Justify your answer. 7. Let (=) = Use the polar form of the Cauchy-Riemann equations to determine where is differentiable. 8. Let g(x,y) - (a) Show that is harmonic in D = {(y): 2 + y + 3) < 4). (b) How can the function () = be used to show that g is harmonic in D? ! 9. Show that ed" = e*+W for any z, w EC. 1