29_Cal_Solution of Calculus_6e

29_Cal_Solution of Calculus_6e - Section 1.4 C01S04.001:...

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Unformatted text preview: Section 1.4 C01S04.001: Because g ( x ) = 2 x increases—first slowly, then rapidly—on the set of all real numbers, with values in the range (0 , + ∞ ), the given function f ( x ) = 2 x − 1 must increase in the same way, but with values in the range ( − 1 , + ∞ ). Therefore its graph is the one shown in Fig. 1.4.29. C01S04.002: Given: f ( x ) = 2 − 3 − x . The graph of g ( x ) = 3 x increases, first slowly, then rapidly, on its domain the set R of all real numbers. Hence h ( x ) = 3 − x decreases, first rapidly, then slowly, on R , with values in the interval (0 , + ∞ ). Hence j ( x ) = − 3 − x increases, first rapidly, then slowly, on R , with values in the interval ( −∞ , 0). Therefore f ( x ) = 2 − 3 − x increases, first rapidly, then slowly, on R , with values in the interval ( −∞ , 2). Therefore its graph must be the one shown in Fig. 1.4.33. C01S04.003: The graph of f ( x ) = 1 + cos x is simply the graph of the ordinary cosine function raised 1...
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This note was uploaded on 09/14/2011 for the course MATH 101 taught by Professor Cheng during the Spring '11 term at Ecole Hôtelière de Lausanne.

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