Banach Spaces

Show that (X, ||*||) is a Banach space if and only if {x in X: ||x||=1} is complete. Know that in the first direction, we must show that {x in X: ||x||=1} is closed subset of X. For the reverse direction, I know I have to take a cauchy sequence and translate it to the unit circle and then show that if it is convergent ther ...continues

Sequences and Limit Superior

Suppose that xn x and the sequence (yn) is bounded. Show that ___ ___ lim (xn + yn) = lim xn + lim (yn). ___ I know that since (xn) converges lim xn = lim (xn) and that ___ __ ___ ...continues

Lagrange Interpolating Polynomials and Kronecker Delta

We are given the Lagrange polynomial in the form: P_n(x)= y_0*L_0(x)+...+y_n*L_n(x) and y_i = f(x_i) and L_i(x)= ((x-x_0)***(x-x_n)) / ((x_i-x_0)***(x_i-x_n)). We must show that L_0(x) + ... + L_n(x) = 1 for all x and n=3. Later we are to generalize this for all n>0. But let's just focus on n=3 for now; I may be able t ...continues

Differentiable and Continuous Functions and Taylor Series (15 Problems)

Please see the attached file for the fully formatted problems. keywords: differentiability continuity

Excel Solver - linear programming model.

Need help with the following problem, am stuck trying to set it up correctly. Can you help with the objective function and constraints, also the formulas for solver. The Arden County, Maryland, superintendent of education is responsible for assigning students to the three high schools in his county. He recognizes the need to ...continues

Transportation Model linear programming model. Need help setting up problem for Excel solver.

Having real problems setting up transportation problems in Excel's Solver. Please help with objective function, constraints, formulas, etc. Spreadsheet would be wonderful soI can see how to do it! The Krampf Lines Railway Company specializes in coal handling. On Friday APril 13, Krampf needed empty coal cars to be moved from ...continues

Need help with Excel Solver Linear Programming Model

Ratings: Course Professor Statistics Management Finance Economics Anderson 90 65 95 40 Sweeney 70 60 80 75 Williams 85 40 80 60 McKinney 55 80 65 55

Numerical Analysis :Sequences and Series

Please see the attached files for the fully formatted problems.

Newton's Method

See attached file for full problem description.

Power Series and Radius of Convergence

Consider the power series ∑anxn for which each coefficient an is an integer. Prove that this series has a radius of convergence, R, where either R=positive infinity or R≤1 See attached file for full problem description.