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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!)
The manager of a specialty store marks up imported products 110%. If a vase imported from Italy costs him $35, what price tag will he put on the item? To ?nd out the price he s
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Find the solution to the subsequent IVP. ty' - 2y = t 5 sin(2t) - t 3 + 4t 4 , y (π) = 3/2 π 4 Solution : First, divide by t to find the differential equation in the accu
The temperature at the point (x, y) on a metal plate is given by the function f(x, y) = x 3 + 4xy + y 2 where f is in degrees Fahrenheit and x and y are in inches, with the origin
a conical vessel of radius 6cm and height 8cm is completely filled with water.a sphere is lowered into the water and its size is such that when it touches the size it is immersed.w
Sheldon as the day for the challenge gets closer wants to enter the race. Not being content with an equal start, he wants to handicap himself by giving the other yachts a head star
1. (a) Give an example of a function, f(x), that has an inflection point at (1, 4). (b) Give an example of a function, g(x), that has a local maximum at ( -3, 3) and a local min
scanning the demographic environment
Q. Assume a birthday is equally likely to occur in each of the 365 days. In a group of 30 people, what is the probability that no two have birthdays on the same day? Solution:
1. Use mathematical induction to prove whenever n is a positive integer. 2. Use loop invariant to prove that the program for computing the sum of 1,...,n is correct.
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