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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.
Illustrates that each of the following numbers are solutions to the following equation or inequality. (a) x = 3 in x 2 - 9 = 0 (b) y = 8 in 3( y + 1) = 4 y - 5 Solution
Recall also which value of the derivative at a specific value of t provides the slope of the tangent line to the graph of the function at that time, t. Thus, if for some time t the
How many ways can six men and three women form a line if no two women may stand behind each other?
Proof of Limit Comparison Test As 0 Now, as we know that for large enough n the quotient a n /b n should be close to c and thus there must be a positive integer
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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.
A differential equation is termed as an ordinary differential equation, abbreviated through odes, if this has ordinary derivatives in it. Similarly, a differential equation is term
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