34_Cal_Solution of Calculus_6e

34_Cal_Solution of Calculus_6e - Chapter 1 Miscellaneous...

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Unformatted text preview: Chapter 1 Miscellaneous Problems C01S0M.001: The domain of f ( x ) = √ x − 4 is the set of real numbers x for which x − 4 = 0; that is, the interval [4 , + ∞ ). C01S0M.002: The domain of f consists of those real numbers x for which 2 − x 6 = 0; that is, the set of all real numbers other than 2. C01S0M.003: The domain of f consists of those real numbers for which the denominator is nonzero; that is, the set of all real numbers other than ± 3. C01S0M.004: Because x 2 + 1 is never zero, the domain of f is the set R of all real numbers. C01S0M.005: If x = 0, then √ x exists; there is no obstruction to adding 1 to √ x nor to cubing the sum. Hence the domain of f is the set [0 , + ∞ ) of all nonnegative real numbers. C01S0M.006: Given: f ( x ) = x + 1 x 2 − 2 x . The only obstruction to computing the number f ( x ) is the possibility that the denominator is zero. Thus we must eliminate from the set of all real numbers those for which x 2 − 2 x = 0; that is, x ( x − 2) = 0. Therefore2) = 0....
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