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1. Study the stability of the limit cycle r=1 for the system given in polar coordinates by the equations r ? =(r^2 -1)(2x-1) , φ ? =1 . (where x=rcosφ ).
2. Solve the equation dy/dx =y+h N , where h N (x)=N for |x-1|<1/2N and 0 for |x-1|≥1/2N with initial condition y(0)=0 , and find the limit of the solution as N→∞ .
3. Prove that δ(αx)=δ(x)/|α| . ( In particular, if α=-1 , we can see δ(x) is an even "function".
Implement a quality management initiative to address the quality management related problem(s) you identified above.
Discrete Structure Assignment: - The Fibonacci numbers are defined as follows: f0 = 0, f1 = 1, and Fn = F n-1 + F n-2 for n >=2, Prove each of the following three claims:
Determine the Minimal Spanning Tree in Graph X using Kruskal's Algorithm. All edges must be labeled from lower to higher named vertices,
Pulani bought a scooter for N$15 000. She paid 15% of the amount in cash as a deposit and signed a hire-purchase agreement to pay the balance in 24 equal monthly instalments.(a) How much did she pay in cash?
3. Entrepreneur of a product estimates that when q units of his items produced every month, the average total profit (in thousand RM) is P ¯(q)= -1.125q+45-200/q. Find the company's maximum profit.
Rectangular trench is to be dug which is to be 240 ft long, 90 ft wide and 9 ft deep. A large dumb truck can carry 20 cubic yards in a load. How many truck loads will be required to remove
Given a prime number, use Generating functions to find the prime number that immediately follows it. For example, if I give a 5, then there will be F(2,3,5) = 7 ; if I give a 11, there will be F(2,3,5,7,11) = 13 ....... (this is a function of all pri..
Show that the functions x and x^2 are orthogonal in P5 with inner product defined by ( =sum from i=1 to n of p(xi)*q*(xi) ) where xi=(i-3)/2 for i=1,...,5.
The topic for the project is Elliptical Paths Of Celestial Bodies although you may choose a different title. The aim is to research ellipses in the context of eccentricities and to use the eccentricities and lengths of the semi-major axis of the p..
Calculate the appropriate test statistic to test the hypotheses.
an instructor in a large lecture class found at the end of the semester that total points scored by students in his
A student inherits 17500 dollars and puts the money in two different accounts. One account earns 5% annually and one account earns 8% annually. She earned a total of 1075 dollars after one year. How much money is in each account?
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