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1. Let f: [a,b] ----> R and suppose f is integrable with respect to alpha. Prove that for any c in the real numbers, cf is integrable with respect to alpha and the integral from a to b of cf d(alpha) = c times integral from a to b of f d(alpha).
Give an example of a function f : [0,1] ----> R such that f is Riemann integrable and f is discontinuous on a dense subset of [0,1].
Find all maximal normal subgroups of Z[p] × Z[q], where p and q are relatively prime. Would the elements from Z[p] have to be one that are relatively prime to q and vice versa?
After t hours on the job, one factory worker is producing Q'1(t) = 60 - 2(t - 1)^2 units per hour, while a second worker is producing Q'2(t) = 50 - 5t units per hour.
A large storage tank, open to the atmosphere at the top and filled with water, develops a small hole in its side at a point 16.0 m below the water level.
Operations Research: Duals Q. Write the dual of this problem, sketch the feasible region of the dual, and find the dual solution graphically
There are 3 boxes. Each box contains several envelopes. Some envelopes have "you lose" written on them. The rest say "you win..." . However, of the ones that say "you win..." , some contain only a piece of paper saying "... nothing" . Each of the ..
Suppose that f_n(0) converges to some number, denoted f(0), and also suppose that the sequence (f'_n) converges uniformly on (0,1) to some function g: (0,1) -> R. Prove that the sequence (f_n) converges uniformly. What is its limit?
A number (a) is called a fixed point of a function (f) if f(a)=a. Prove that, if f'(x) does NOT equal 1 for all real numbers (x), then f has at most one fixed point.
Numerical Concepts : Definitions, Please explain or define these concepts. 1. Natural number 2. Multiplication 3. Subtraction 4. Closure for addition
Show that if @:R -> S is a ring homomorphism, then the ker(@) is an ideal of R and that @ is injective if.
Using the given data and chart, find the coefficients a, b, and c of the exponential model algebraically.
Linear Regression features to find the equation for V.
Using a 0.025 significance level, test the claim that the proportions of agree/disagree responses are same for the subjects interviewed by men & the subjects interviewed by women.
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