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2 (a) Define uniform continuity on R for a function f R → R (b) Suppose that f,g R → R are uniformly continuous on R (i) Prove that f g is uniformly continuous on R (ii) Give an example to show that fg need not be uniformly continuous on R Solution • (a) A function f R → R is uniformly continuous if for every ϵ > 0 there exists δ > 0 such that f(x)−f(y) < ϵ for all xCentOS56 C X g CentOS56 ݒX Check the box if the filing relates solely to preliminary communications made before the commencement of a tender offer Check the appropriate boxes below to designate any transactions to which the statement relates x thirdparty tender offer subject to Rule 14d1 o issuer tender offer subject to Rule 13e4
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Proofs Homework Set 1 MATH 217 — WINTER 11 Due January 12 Logical Connectives Every mathematical statement is either true or false Starting from given mathematical statements, we can use logical operations to form new mathematical statementsExample 5 X and Y are jointly continuous with joint pdf f(x,y) = (e−(xy) if 0 ≤ x, 0 ≤ y 0, otherwise Let Z = X/Y Find the pdf of Z The first thing we do is draw a picture of the support set (which in this case is the firstFIRSTDEGREE EQUATIONS AND INEQUALITIES In this chapter, we will develop certain techniques that help solve problems stated in words These techniques involve rewriting problems in the form of symbols
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