Pre-Calc Homework Solutions 35

# Pre-Calc Homework Solutions 35 - Section 1.6(e(b Amplitude...

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(e) [ 2 1, 13] by [ 2 10, 100] 35. (a) Amplitude 5 37 (b) Period 5 } (2 p 2 / p 365) } 5 365 (c) Horizontal shift 5 101 (d) Vertical shift 5 25 36. (a) Highest: 25 1 37 5 62 8 F Lowest: 25 2 37 52 12 8 F (b) Average 5 } 62 1 2 ( 2 12) } 5 25 8 F This average is the same as the vertical shift because the average of the highest and lowest values of y 5 sin x is 0. 37. (a) cot ( 2 x ) 5 } c s o in s ( ( 2 2 x x ) ) } 5 } 2 co si s n ( x ( x ) ) }52 cot ( x ) (b) Assume that f is even and g is odd. Then } g f ( ( 2 2 x x ) ) } 5 } 2 f ( g x ( ) x ) }52} g f ( ( x x ) ) } so } g f } is odd. The situation is similar for } g f } . 38. (a) csc ( 2 x ) 5 } sin ( 1 2 x ) } 5 } 2 si 1 n( x ) }52 csc ( x ) (b) Assume that f is odd. Then } f ( 2 1 x ) } 5 } 2 f 1 ( x ) }52} f ( 1 x ) } so } 1 f } is odd. 39. Assume that f is even and g is odd. Then f ( 2 x ) g ( 2 x ) 5 ( f ( x ))( 2 g ( x )) 52 f ( x ) g ( x ) so ( fg ) is odd. 40.
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