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Fundamental Theorem of Calculus, Part I If f(x) is continuous on [a,b] so, g(x) = a ∫ x f(t) dt is continuous on [a,b] and this is differentiable on (a, b) and as,
Patrick has a rectangular patio whose length is 5 m less than the diagonal and a width which is 7 m less than the diagonal. If the field of his patio is 195 m 2 , what is the lengt
tom has 150 feet of fencing to enclose a rectangular garden. if the length is to be 5 feet less than three the width, find the area of the garden
Suppose that at some future time every telephone in the world is assigned a number that contains a country code, 1 to 3 digits long, that is, of the form X, XX , XXX or followed
On a piece of machinery, the centers of two pulleys are 3 feet apart, and the radius of each pulley is 6 inches. Determine the size of belt (in feet) is required to wrap around bot
A card is drawn from a well shuffled deck of cards (i) What are the odds in favour of getting spade? (Ans: 1:3, 3:1, 3:10, 1:25) (ii) What are the odds against getting a spa
lnx(1+x)
Bikes are on sale for 30% off the original price. What percent of the original price will the customer pay if he gets the bike at the sale price? The original price of the bike
Marc goes to the store with exactly $1 in change. He has at least one of each coin less than a half-dollar coin, but he does not have a half-dollar coin. a. What is the least nu
Assume that (X, d) is a metric space and let (x1, : : : , x n ) be a nite set of pointsof X. Elustrate , using only the de nition of open, that the set X\(x1, : : : , x n ) obtain
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