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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.
1 what does a point estimate tell you about the population proportion? why does a sample proportion tend to be an
Let A and B be sets. Show that A x B and B x A have equal cardinality by constructing an explicit bijection between the two sets. Then use the following proposition to prove that multiplication is commutative. (Let n, m be natural numbers. Then nx..
Use the simplex method to determine the optimal production schedule so as to maximize profits. Show that the geometric method gives the same solution.
Graph the function using the equation in part a. Explain why it is not necessary to plot points to graph when using y = a (x - h) 2 + k.
case study applications paper choose one of the following case studiesbull food websbull coding theorybull network
The shaper is available for 120 hours, and the grinder is available for 110 hours. No more than 200 units of component3 can be sold, but up to 1000 units of each of the other components can be sold.
Suppose instead that the signal is being broadcast from the other side of the Milky Way Galaxy, about 70000 light-years away. How large a radio telescope would we need to detect this signal?
find an ad from a newspaper,the internet,telephone book,sales paper, magazine or another source that advertise products were you can apply your knowledge of slope.
Important information about Working with conditional probability. The following table shows frequencies for red-green color blindness, where M represents "person is male" and C represents "person is color-blind".
1 write a program that allows a user to enter a line of text counts number of words and number of vowels in the
snell's law total internal reflection between two materials is seen to occur if a critical angle of 60° is exceeded. if the index of refraction of the material that the light is entering is 1.98, find the index of refraction of the material in whi..
It travels 430 going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current?
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