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mac1140_lecture1_2 - L1 1.1 Real numbers and their...

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1 L1 § 1.1 Real numbers and their properties Expressions of the form a b . We will be dealing with fractional expressions on a regular basis. Here are two important questions: 1. When is the fractional expression undefined ? Answer : When the denominator 0 b = (division by 0 is undefined). Note: As more situations arise, there will be more restrictions such as when taking square roots. 2. When is the fractional expression equal to zero ? Answer : When the numerator 0 a = , provided the denominator 0 b . A word of caution : 0 0 is not a number! Therefore, a number that makes an expression equal to 0 0 does not make it equal to 0. 2 Example . a) Find the value of x so that 2 3 4 x x + is undefined. b) Find the value of x so that 2 0 3 4 x x = + . Example . a) Find the value of x so that ( 3) x x x is undefined. b) Find the value(s) of x so that ( 3) 0 x x x = . Note : In this example we could cancel out the x ’s to get just ( 3) x , but we still have the restriction: 0 x . This will be discussed in detail in sections 1.5 and 4.5.
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