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Prove that f must have a fixed point; that is, show f(x)=x for at least one value of x belong to [0,1].
Find the conjugacy classes of D8.Show that the rotations in D8 form a normal subgroup
A function is increasing on A if f(x)<=f(y) for all x
Prove that if f:A->R and a limit point c of A , lim f(x)=L as x->c if and only if lim f(x)=L as x->c^-(left handed limit) and lim f(x)=L as x->c^+(right handed
If lim f(x) as x->c does not exists for some other reason the discontinuity at c is called essential discontinuity.
Let g:[0,1]->R be twice-differentiable (i.e both g and g' are differentiable functions) with g''(x)>0 for all x belong to [0,1].if g(0)>0 and g(1)=1.
Calculate the objective function value for the sequence of customers of 1 to 8 to minimize the total time in system.
Show that the function g(x){x/(2+x^2 sin(1/x)) if x not=0 0 if x=0 is differentiable on R and satisfies g'(0)>0.
If g'(c)not= 0 show that there exists a delta neighborhood V_delta (c) subset or equal to (a,b) for which g(x) not= g(c) for all x belong to V_delta (c).
Prove that lim inf a_n<=lim sup a_n for every bounded sequence and give example of a sequence which the inequality is strict.
Setup a network Flow for this Problem using nodes and links but do not solve for optimal solution
Prove that (sn) is a convergence sequence. Hint: To show (sn) is Cauchy, first show that |sn+1 - sn| = a?|sn - sn-1| for n = 1.
Sensitivity Analysis and LP solve.There are three warehouses at different cities: Tauranga,
By an n-fold line subdivision of the plane P, we mean any collection of n-distinct (infinite) lines in P, together with the open regions in P.
If |z|>R, the terms of the series are unbounded and the series is consequently divergent.
What is the minimum cost attainable under the optimal plan?The company has located a third supplier (New-Supplier)
How would you define the arc parameters and demand node parameters in order to find the shortest path through this network
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.