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The division algorithm says that when a is divided by b, a unique quotient and remainder is obtained. For a fixed integer b where b ≥ 2, consider the function f : Z → Z given by f(a) = r where r is the unique remainder obtained when a is divided by b.
(a) What is the range of f? Based on your answer, is f onto?
(b) Determine whether f a 1-1 function.
Suppose that the probability of your favorite baseball player getting a hit at bat is 0.45. Assume that each at bat is independent. What is the probability that he bats eight times
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Optimization : In this section we will learn optimization problems. In optimization problems we will see for the largest value or the smallest value which a function can take.
Find out all the critical points for the function. Solution Following is the derivative for this function. Now, this looks unpleasant, though along with a little fa
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