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Let {f_n} be a sequence of measurable functions on [0,1] with |f_n (x)| < infinity for a.e x. Show that there exists a sequence c_n of positive real numbers such that f_n (x) / c_n -------> 0 a.e.x
Hint: Pick c_n such that m ({x : |f_n (x) / c_n| > 1/n} ) < 2^(-n), and apply the Bore-Cantelli Lemma
Let X be a subset of R, let E be a subset of X, let x_0 be an adherent point of E, and let f: X-->R, g: X-->R, h: X-->R be functions such that f(x)
Find the mean values for this variable.
In your own words, explain the difference between intersecting and perpendicular lines. Can two lines exist that are not intersecting or parallel? Explain your answer.
Find an equation in the form y=ms +b (where possible) for each line. Solve each system of equation. Let z be the parameter.
Formulate a linear programming model for the problem.
A matrix A is said to be skew-symmetric if A^T = -A. Show that any square matrix can be represented as a sum of a symmetric matrix and a skew-symmetric matrix.
Find the solution of the given linear equation - Evaluate the time and the height at which she opens her parachute.
Solve the problem of Critical Path and PERT. A PERT project has 45 activities, 19 of which are on the critical path. The estimated time for the critical path is 120 days. The sum of all activity variances is 64, while the sum of variances along the..
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Probability- Considering Failure Rates, The records of Midwestern University show that in one semester, 38% of the students failed mathematics, 27% of the students failed physics
Maximizing Profit: Demand for Steak Dinners, The unit cost of producing a steak dinner at the Smalltown Inn is $6. If a restaurant charges p dollars for a steak dinner, customers will demand 200 - 5p steak dinners per week
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