Let xk = (-1)k for any positive integer k. Let f(n) = (x1 + x2 + … + xn)/n, where n is a positive integer. Give the range of this function.
If f(n) is a function such that f(1) = f(2) = f(3) = 1, and such that:
for n > 3, then f(6) is equal to:
Consider the numbers Fn defined by the following formula:
where n may be any positive integer. Calculate F1 through F5. Do you notice anything suprising?
Suppose that the functions f(x) and g(x) have the following graphs:
Find the graph which most resembles the graph of |f(x) – g(x)|.
If the postal rate for first class letters is 42 cents for the first ounce or any portion thereof, and 17 cents for every ounce or portion thereof after the first ounce, then find the cost of a letter weighing w ounces, where w is some positive real number. Use [x] to stand for the greatest integer in w, as usual.
This problem has been attributed to Sir Isaac Newton. Three cows eat in two weeks all the grass on two acres of land, together with all the grass that grows there in the two weeks. Two cows eat in four weeks all the grass on two acres of land, together with all the grass that grows there in the four weeks. How many cows, then, will eat in six weeks all the grass on six acres of land together with all the grass that grows there in the six weeks? Assume that the quantity of grass on each acre is the same when the cows begin to graze, that the rate of growth is uniform during the time of grazing, and that the cows eat the same amount of grass each week.
When Homer Smith and his wife Okla flew to Rome, they had together 94 pounds of baggage. Homer paid $15.00 and Okla paid $20.00 for the excess weight of their baggage. If Homer had made the trip by himself with the combined baggage of both of them, he would have had to pay $135.00 for excess baggage. How many pounds of baggage can one person take along without charge?
Define an operation $ for positive real numbers so that a $ b = ab/(a + b).
Then 4 $ (4 $ 4) = what?