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380_takehome_quiz4[1]

# 380_takehome_quiz4[1] - z j< 3 What is I j z j =1 f z z...

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Math 380 Take-home Quiz Due in class Friday, April 30 Name Ground rules. You must do this exam in one sitting by yourself. Do not discuss the problems with anyone between 10 pm April 18 and 10 am April 30. You may use your notes and textbook only. 1. (2 pts) Calculate I j z j =3 z 2 z 2 + 3 z ° 4 dz 2. (3 pts) Suppose f ( z ) = X 1 k = °1 a k z k where the series converges on the annulus 0 <
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Unformatted text preview: z j < 3 : What is I j z j =1 f ( z ) z 10 dz in terms of the a k ? 3. (2 pts) Find the &rst three non-zero terms of the Maclaurin seris for e z sin z without computing deriv-atives of e z sin z: 4. (3 pts) Find the annulus of convergence of the following Laurent series: 1 X k =1 1 2 k z k + 1 X k =0 z k 2 k : 1...
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