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# Question 1 (a) (5 marks) Find the Laurent series expansion off(z)at z = 1. On which domain does the series converge? (b) 5 marks) Without writing down the expansio...

## Question

###### Question 1 (a) (5 marks) Find the Laurent series expansion off(z)at z = 1. On which domain does the series converge? (b) 5 marks) Without writing down the expansion, find the radius of convergence for the Taylor series of f(z) = Log(z) + Log(iz) at z = -l+i.

Question 1 (a) (5 marks) Find the Laurent series expansion of f(z) at z = 1. On which domain does the series converge? (b) 5 marks) Without writing down the expansion, find the radius of convergence for the Taylor series of f(z) = Log(z) + Log(iz) at z = -l+i.  #### Similar Solved Questions

##### SNOW A call-in poll where 200 listeners responded with their opinion on driving in snow estimated with 95% confidence that the proportion of people in the community who hate it is between 33.29 and 46.89/.Find the mistakel
SNOW A call-in poll where 200 listeners responded with their opinion on driving in snow estimated with 95% confidence that the proportion of people in the community who hate it is between 33.29 and 46.89/. Find the mistakel...
##### Thermometer made of Platinum has a resistance of 50 Q at 20 C, what is the measured temperature (in units of C) when its resistance is 79 Q_ Assume the temperature coefficient of resistivity to be & = 3.92X10-3 C-1Select one: A. 167.96B. 638.16C. 147.96D. 109.96E. 403.06
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##### Question 62 ptsLet X be normally distributed with the variance Var-2. We sample X and determine the 98% confidence interval for the mean p. How large should bethe sample size nto ensure that / is estimated within0.5 or less?
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##### Use the t-distribution and the given sariple results comciele tcicstol the Flenrpotncscs Assue thcreslts cone from random samplcs andMf the sample sizes JSSUMe the underlying distributions are relativcly nocmnaTest Huvs /a("3 using the sample results T 56,84 32 with /a SWandli 51441 6 9 with n;(a) Glve the test statistic and thc p-valueRound your answcr for Ulia teststatistic two dccimal placcs aadvolt answcr Ior the p-value Enrcc dccimal placesMhttu Ep-ullWlentheccnacnnchctonTcsalseaclReje
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##### Consider the Lewis structure for the polyatomic oxyanion shown below, where $X$ is an element from the 3rd period (Na- Ar). By changing the overall charge, $n$, from $1-$ to $2-$ to $3-$ we get three different polyatomic ions. For each of these ions (a) Identify the central atom, $mathrm{X}$.(b) Determine the formal charge of the central atom, $mathrm{X}$. (c) Draw a Lewis structure that makes the formal charge on the central atom equal to zero. (d) If the Lewis structure you drew in part (c) di
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##### Evaluate the following indefinite integrals using substitution method: 2x3 (a) dx pts) (7-2x4)500n "ernow %e; Ecpl4Er6 Neuwnrdue 07
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##### The objective lens of the refracting telescope at the Lick Observatory in California has a focal length of $57 \mathrm{ft}$. a. What is the refractive power of this lens? b. What focal length (mm) eyepiece would give a magnification of $1000 \times$ for this telescope?
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##### Activity 3: Equipotential surfacesUse you measuring tape and the digital voltmeter you used in the previous activity and fillin the tableC1C2 D1: you PredictionC3 C4 D2-Your D1 x V measurementC5 D2 x VC6 CS/(charge used)12.32 7.93 7.32 5.21 4.71 3.83Question (Brief answers)A) What formula have you used to generate C2 ?3B) Compare C1 with C2 How does your prediction compare with Your measurement ?3C) Compare C4 with C5 How do the data in the two columns compare ?3D) What is C6 ?3F) Calculate the
Activity 3: Equipotential surfaces Use you measuring tape and the digital voltmeter you used in the previous activity and fillin the table C1 C2 D1: you Prediction C3 C4 D2-Your D1 x V measurement C5 D2 x V C6 CS/(charge used) 12.32 7.93 7.32 5.21 4.71 3.83 Question (Brief answers) A) What formula h...
##### 3. Two examples of silica materials are quartz and silica gel.a. How are the structure and property differences of thosematerials? (20) b. Silica gel can be prepared through the sol-gelprocess by using precursor of TEOS (Si(OC2H5)4) or sodium silicate(Na2SiO3). What is the difference in the process of preparingsilica gel using those different precursors? Explain shortly(20)
3. Two examples of silica materials are quartz and silica gel. a. How are the structure and property differences of those materials? (20) b. Silica gel can be prepared through the sol-gel process by using precursor of TEOS (Si(OC2H5)4) or sodium silicate (Na2SiO3). What is the difference in the proc...
##### 14. (a) If a, b are integers and a^2| b^2, prove that a |b.Hint. An integer c divides an integer d if and only if themultiplicity of every prime p inside the unique factorization of cis less than or equal to the multiplicity of p in the uniquefactorization of d.(b) If a, b are coprime integers and ab is a perfect square(i.e. ab = c^2 for some integer c, show that a and b are perfectsquares.Hint. Two integers c, d are coprime if and only if no prime canappear in the unique factorizations of both
14. (a) If a, b are integers and a^2| b^2, prove that a | b. Hint. An integer c divides an integer d if and only if the multiplicity of every prime p inside the unique factorization of c is less than or equal to the multiplicity of p in the unique factorization of d. (b) If a, b are coprime integers...