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There is a nonempty set S in R such that closure of S is equal to R and the closure of its complement closure(R-S) also is equal to R.
Determine a simple real-life example scenario to solve systems of linear equations
Using forecasting models in business operations.Describe how a domestic fast food chain like McDonald's with plans for expanding into China
Formulating a nonlinear program for profit maximization.A bakery produces muffins and doughnuts. Let x1 be the number of doughnuts
Prove that the function f(x) = e^x is differentiable on R, and that (e^x)' = e^x. ( Hint: Use the definition of e^x, and consider the sequence of partial sums.)
Let a R be continuous on [a,b] and differentiable on (a,b). If f(a) 0.
Identify the sensitivity ranges for the profit of a sausage biscuit and the amount of sausage available. Explain the sensitivity ranges.
Let I:=[a,b] be a closed bounded interval and let f:I->R be continuous on I. Then f has an absolute maximum and an absolute minimum on I.
Formulate and solve the LP to find the least-cost means of shipping supplies from the factories to the warehouses.
Verify that Gregory’s series is correct by using a Taylor Series expansion or methods of power series.
Space Constrained Inventories.A grocer has exactly 1,000 square feet available to display and sells 3 kinds of vegetables.
Determine whether each of these infinite series are convergent or divergent. Justify your answer.
Consider the real linear map.Compute det(A sub alpha) and det (A sub alpha bar). Interpret.
Let X = (xn) and Y = (yn) be sequences of real numbers that converge to x and y respectively, and let c be an element R.
Multiply the three matrices together in order (A*B*C) to get a fourth matrix 'D'. What is the fourth matrix?
F(x)=square root 4+x and G(x)=square root 1+x by writing square root of 4+x=2 square root 1+1/4x and using substitution in one of the standard Taylor series.
Solve the system of equations by the Gaussian elimination method.
Let f, g be defined on A ? R to R , and let c be a cluster point of A. Suppose that f is bounded on a neighborhood of c and that limx?c g =0.
Discrete Math: Matrix Operations (Proofs).Prove or disprove that, for matrices A,B,C for which the following operations are defined:
Evaluate the determinant by expanding by cofactors..Solve the system of equations by the Gaussian elimination method.
How would economic pressures like inflation or deflation affect your decision to make a long term investment?
Working with matrices : Determinants and transposes. If A is a 3x3 matrix such that the determinant A is 2 and A1 is the transpose of A
Suppose X is a measurable space, E belongs to the sigma algebra ( I believe to the sigma algebra in X) , let us consider XE = Y.
Using the method of undetermined coefficients, find the solution of the system:
Let u = x + y/ 1-xy and v = tan-1x + tan-1y . If xy?1 , show that u and v are functionally related and find the relationship.