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1. Find the Taylor series expansion of the function f (z) = 1-z/1+z centered at 0, using two methods
a) By direct application of the coefficient formula. Produce three terms of the expansion
b) Without the direct application of the coefficient formulae.
c) Giving the required reasoning, find the radius of convergence.
2. Derive the Laurent series expansion of the function f (z) = 1/z2 centered at 1 and convergent on the annulus 1 < |z-1| < ∞.
3. Find the Taylor series expansion of the function f (z) = 1/(1-z)3 centered at 0. Find the radius of convergence explaining all your steps.
A poster is to have an area of 220 in2 with 1 inch margins at the bottom and sides and a 3 inch margin at the top. What dimensions will give the largest printed area?
Calculate the standard deviation
Early one morning it began to snow at a constant rate. At 7 AM a snowplow set off to clear a road. By 8 AM it had traveled 2 miles but it took two more hours for the snowplow to go another 2 miles.
A certain drug is made out of two compounds only: compound A and compound B. To make this drug, two parts of compound A are used for every three parts of compound B. If a chemist wants to make 315 milliliters of this drug, how many milliliters of ..
In some chemical reactions, the rate at which the amount of a substance changes with time is proportional to the amount present. For the change of -glucono lactone into gluconic acid, for example, when is measured in hours.
A garden table and a bench cost $600 combined. The cost of the garden table is three times the cost of the bench. What is the cost of the bench?
in the course of designing theater seats the sitting heights in mm of a sample of adult women is obtained and the
A farmer wants to set aside a rectangular plot of land to contain 580 square meters. If the width is 19 less than the length, find the dimensions of the plot.
To accomplish this reduction, management decides that the new bar should have teh same 3-cm thickness, but the length and width of each should be reduced an equal number of centimers. What should be the dimensions of the new candy bar?
Sam Allen is a parent of several students at Mattson Area High School in a small community southwest of Dallas, TX. He is investigating different ways to finance his daughter's first year at Southwest Texas State University - and he is considering le..
Seven Marching Bands will perform at a competition. The order of the performances is determined at random. What is the probability that the bands will perform in alphabetical order by school name?
Summarize each method, and discuss how the financial information is used to make a particular decision. Provide a scenario in a health care situation in which a given method of analysis might be used.
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