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Unformatted text preview: 05/17/2002 FRI 09:38 FAX 6434330 MOFFITT LIBRARY 001 Midterm #1
Math 121A (Section 2) — Fall 2001 'T‘cakmoth Each problem counts 10 points Problem # 1. Find all solutions of the equation
Z3 i —8%} write them in a polar (|z|ei“g("‘)) and rectangular (Re(z) +i1m(z)) forms and plot them in the complex plane. Problem #79 2. Find the sum of the series 0M6+i%_bdﬁ+ﬂ3+Uﬂﬁ+ﬂ5+u£:§:b%wﬁﬂ6+ﬂhﬂ
72:0 3! 5! Qn+1ﬂ and write it in a rectangular form R.e(z) + iIm(z). Problem # 3. Find the ﬁrst three terms of the two—variable Maciaurin series for
l —1— x23; ' Write down both the derivation and the ﬁnal answer! Problem # 4. (a) Derive the formula Minn—1(2) 2 éln 1+ Z 1_z from the deﬁnition of tanh z (or deﬁnitions of sinhz and cosh z). (b) Use the derived formula to compute temhﬁ1 (i) I 05/17/2002 FRI 09:39 FAX 6434330 MOFFITT LIBRARY 002
Problem # 5. Find the interval of convergence of the following series (including end points tests! ): Justify your answer by mentioning the theorems/ tests that you use to draw con-
clusions about convergence, and state explicitly if the convergence is absolute or conditional. Problem # 6. Compute dz/dt given 2 = my,
y : tent. Problem # 7. Does the following series converge? i713 w lnn
“:1 2” + 1071 Justify your answer by mentioning the theorems/ tests that you use to draw conclu— sions about convergence. ...
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This note was uploaded on 11/21/2009 for the course MATH 121a taught by Professor Staff during the Fall '08 term at University of California, Berkeley.
- Fall '08