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Assume that (X, d) is a metric space and let (x1, : : : , xn) be a nite set of pointsof X. Elustrate , using only the de nition of open, that the set X\(x1, : : : , xn) obtained by removing every xi from X is open in X. (Sketch a picture to get some intuition!)
a local pizza store offers medium two-topping pizzas delivered for $6.00 per pizza plus a $1.50 delivery charge per order. on weekends, the store runs a game day special: if six or
an insurance salesman sells policies to 5 men, all of identical age in good health. the probability that a man of this particular age will be alive 30 years hence is 2/3.Find the p
PROOF OF VARIOUS INTEGRAL FACTS/FORMULAS/PROPERTIES In this section we've found the proof of several of the properties we saw in the Integrals section and also a couple from t
Express the product of -9p3r and the quantity 2p - 3r in simplified form. The translated expression would be -9p3r(2p - 3r). Noticed that the key word product means multiply.
Absolute Convergence While we first talked about series convergence we in brief mentioned a stronger type of convergence but did not do anything with it as we didn't have any
what is the value of integration limit n-> infinity [n!/n to the power n]to the power 1/n Solution) limit n-->inf. [1 + (n!-n^n)/n^n]^1/n = e^ limit n-->inf. {(n!-n^n)
what is division
carlie is now fivetimes as old as henry. in nine years her age will be twice henry''s age then. how old is carly now
Fermat's Theorem If f(x) has a relative extrema at x = c and f′(c) exists then x = c is a critical point of f(x). Actually, this will be a critical point that f′(c) =0.
John and Charlie have a whole of 80 dollars. John has x dollars. How much money does Charlie have? This problem translates to the expression 42 + (11 - 9) ÷ 2. Using order of o
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