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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.
A number, x, increased through 3 is multiplied by the similar number, x, increased by 4. What is the product of the two numbers in terms of x? The two numbers in terms of x wou
Example of Adding signed numbers: Example: (2) + (-4) = Solution: Start with 2 and count 4 whole numbers to the left. Thus: (2) + (-4) = -2 Adding
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Graph f ( x ) = e x and g ( x ) = e - x . Solution There actually isn't a lot to this problem other than ensuring that both of these exponentials are graphed somewhere.
Find the amount of sheet metal need to form a conical funnel of base radius 30cm with a vertical height of 50cm, allowing for 0.5cm overlap. Find the total surface area?
So far we have considered differentiation of functions of one independent variable. In many situations, we come across functions with more than one independent variable
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How many ways can 4 DVDs be arranged on a shelf? Solution: There are 4 ways to choose the first DVD, 3 ways to choose the second, 2 ways to choose the third and 1 way to choo
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About Zeros in the Denominator of Rational Expressions One thing that you must be careful about when working with rational expressions is that the denominator can never be zero
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