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Math 121A - Fall 2001 - Borcherds - Midterm 1

# Math 121A - Fall 2001 - Borcherds - Midterm 1 - THU 09:34...

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Unformatted text preview: 04/25/2002 THU 09:34 FAX 6434330 MOFFITT LIBRARY Fall 1001 Paste/550:1 Borchercls let, Mlci‘term Math 121Amidterm, Thursday September 27, 9:40-11:00. Please make sure that your name is on everything you hand in. You are allowed calculators and 1 page of notes. Answer as many questions as you can. All questions have about the same number of marks. . Test the series 220:1n/(n2 —|— 1), 2:12 1/nlog(n) and 2:0: 110071/711 for convergence. 3:3 3 . Evaluate limmHoﬂ — e )/r . Express each of the following complex numbers in the form a —|— 3'?) for a and 1) real: (1 + i)/(2 + 2'), (1 + Q10, 837ri/2. . Evaluate 1 -+- cos(6’) + cos(29) + - - ~ + cos(n6). . If x3 +ay— ~— b and y3 + 0:12 — a ﬁnd (833/80,)5, (ax/8a)y, (act/3513);, b, (Ba/div” at (.T 31,0, 3)) =(— 1, 2 3, 5). . If 3:89 2 ye”: ﬁnd dy/da: and dZy/da:2 for y 5:5 1. Find all possible values of 2'1“. Find a formula for cos(5(9) as a polynomial in cos(6) and sin(9). I001 ...
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