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Linear Spaces, Mappings and Dimensional Spaces.Show that if dim X = 1 and T belongs to L(X,X), there exists k in K st Tx=kx for all x in X.
Find matrices representing the linear transformations ? and d.
Find the average rate of change for the function f(x) = 4/(x+3) between the values of 1 and x.
A heated object is allowed to cool in a room temperature which has a constant temperature of To.Analyse the cooling process.
Find the Limit x?0 f(x) Explain why L'Hopital's Rule cannot be used to find the limit of Lim x?0 e^2x/x
Obtain the state-space representation of the system in terms of the new variables.
Assume that half of the 100,000 covered lives in the commercial payer group will be moved into a capitated plan.
An elliptic curve can be written as y^2=x^3+ax+b. I need a proof for why x^3+ax+b either have 3 real roots or 1 real root and 2 complex roots.
Can we use this definition to find the adjoint of T (T is given at the end)? This part is the additional information to solve the question above;
Determine whether the series, infinity is absolutely convergent, conditionally convergent or divergent.
Test the series for convergence or divergence by using the Comparison Test or the Limit Comparison Test.
Prove that every infinite and bounded point collection in the plane (R2) has a limit point.
Show that the nth derivative of f(x) exists for all n ? N. Please justify all steps and be rigorous because it is an analysis problem.
Prove that there exists a constant Ca such that log x = Caxa for all x ? [1,8), Ca ? 8 as a ? 0+, and Ca ? 0 as a ? 8.
Since this problem is an analysis problem, please be sure to be rigorous. It falls under the chapter on Integrability on R, where they define partition.
What is the maximum of F = x1 + x2 + x3 + x4 on the intersection of x21 +x22 +x23 + x24 = 1 and x31+ x32+ x33+ x34= 0?
Write a composition series for the rotation group of the cube and show that it is indeed a composition series.
Find MacLaurin Series for the given function f. Use the linearity of the Laplace Transform to obtain a series representation L(f)=F(s)
Prove that f(x)<=0 for all x in [a,b]. Is this true if we require only integrability of the function?
How can I provide a geometric interpretation of this formula in terms of areas and then prove this formula.
Linear Programming Model for Maximizing Profit of a Production Schedule
Suppose that the function f:[0,*)->R is continuous and strictly increasing, with f(0) = 0 and f([0,*)) = [0,*).
Maximizing the Revenue for an Airline Company.An airline has a new airplane that will be fitted out for a combination of first and second class passengers.
Let f:[a,b] mapped to the Reals be a function that is integrable over [a,b], and let g:[a,b] mapped to the Reals be a function that agrees.
Use mean value theorem to prove that (inf U(f,g,p), for p is element of P) = (sup L(f,g,p), for p is element of P) = ( INTEGRAL f(x)g'(x)dx, as x from a to b)