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(b) True or false: if I is the unit circle traversed once counterclockwise, then J. z...
2. (a) Evaluate the contour integral z dz, where I is the circle 12 – 11 = 2 traversed once counterclockwise.
1 5. Let A = dz, (2 – 1)2(2 + 2i)3 where I is the circle [2] = 3 traversed once counterclockwise. The following is an outline of the proof that A = 0, justify each statement. Jo Tz – 1)*(x + 2133 (a) For R > 3 show that A = A(R) where A(R) Som 1 (z – 1)2(x + 2i)3 dz, and I'R is the circle (2|| = R traversed once counterclockwise. 21R (b) For R > 3...
Please only do 8. 7. Compute fr Re zdz along the directed line segment lL llomん 8. Let C be the perimeter of the square with vertices at the points z = 0, z = 1, z = 1 + i, and z = i traversed once in that order. Show that ez dz = 0. 1, where 7. Compute fr Re zdz along the directed line segment lL llomん 8. Let C be the perimeter of the square with...
Please answer any of the questions. Thank you! (B) True/False For full credit, please (1) circle True or False for each question and (2) below each question, justify why (in your own words) your answer is the best choice based on concepts from virology. (2 points each) 13. True or False: The genome of a virus can be composed of RNA or DNA, but only in double-stranded forms. 14. True or False: The different types of viral genomes all use...
11. Circle true or false. No justification is needed. (14 points) (a) If f(x) - o(g(x), and both functions are continuous and positive, then fix dz converges. TRUE FALSE (b) If f(x)- o(g(x)), then f(x)gx)~g(x). TRUE FALSE (c) If the power series Σ an(x + 2)" converges atェ= 5, then it must km0 converge at =-6. TRUE FALSE (d) There exists a power series Σ akz" which converges to f(z)-I on some interval of positive length around FALSE TRUE (e)...
2 +1 (b) Evaluate the contour integral dz, 22 – 9 where I is the boundary of the square D = {z E C:-4 < Re(z) < 4, -4 < Im(z) < 4} traversed once counterclockwise.
(1 point) Let F = (9x+y + 3y2 + 4er) i + (Sex2 + 324x) j. Consider the line integral of F around the circle of radius a, centered at the origin and traversed counterclockwise. (a) Find the line integral for a = 1. line integral = (b) For which value of a is the line integral a maximum? (Be sure you can explain why your answer gives the correct maximum.)
The Fourier coefficient b, of the periodic function J (*) I for - Sx<0 for 0 SXst is: Select one: a. 2 s(x) - 2* + 4 cosa – cos 2x +cos3x - cos 4x +...+2)-1,7 is the Fourier series of a neither even nor odd periodic function. Select one True O False dz = ... where C is the circle - JC-_2 Select one: o a. 4ni ob. 8ni O co od 2ni If the function f(z) = u(x,...
(16 points) For each of the statements below, circle True if you think it is true, and circle False if you think it is false. You may use the space to do scratch work, but no partial credit will be awarded on this question. (4 points for each statement.) (a) True False The vector field F3)defined on all of R2, iscservative. (b) True False The veetor field F defined on R2 minus the origin, is conservative (c) True False A...
I. True or False. Specify whether the statements are true or false. You will receive an extra 25% for false statements that are corrected or explained (must use appropriate vocabulary for the explanation to be considered). Underline and rewrite the false portion with the corrected word/phrase/explanation in the blank provided (must be completely correct for extra credit). (2 points each; total of 12 points) (9,10, 11, 12,17} and Bs(10, 11,17), then BCA. 2. IfA= 3. (6,8,10) (5,6,7,8,10