# E1RevAns - f(1 = 3 f x is continuous from the left at 0 and...

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Review Answers– Exam 1 1. Clockwise from top left corner: 5 4 , 3 2 , + , 12 , - 1 , 0 2. Problem should also say that x is an angle in Quadrant I: - 5 3 and - 13 84 respectively 3. 4 4. 0, ± π , ± π 4 , ± 3 π 4 5. (0 , 1 2 ] 6. In order from left to right: ( -∞ , 0) [2 , ) , x 6 = 0 , 4 , x > 0 and x 6 = e 2 7. g ( f ( x )) = 1 + x 2 + x with domain ( - 2 , ) 8. r = 2 and s = 6 9. First equation: x = 3; Second equation: x = 6 10. See the graphs in our notes and text. 11. f - 1 ( x ) = 4 + e x - 2 and the limit is -∞ 12. To help with the graphs: f ( x ) is x 2 - 1 when x 1 and 1 - x 2 when x < 1 g ( x ) has the graph of cot( x ) moved right π 2 , reﬂected across the x -axis, and stretched along y -axis by factor 3 k ( x ) has the graph of h ( x ) moved left 3, compressed along x -axis by factor 2, reﬂected across the x -axis, and moved up 2 13. The limits at 2, 1, and 0 are: 0, 3, and “does not exist” respectively. f ( x ) has a removable discontinuity at x = 1 that is removed by deﬁning

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Unformatted text preview: f (1) = 3. f ( x ) is continuous from the left at 0, and from neither the right nor the left at 1. 14. a) -64 units/sec b) -32 units/sec c) y = -32x+64 15. The limits in order are 2,-∞ , + ∞ . f ( x ) has an inﬁnite discontinuity at x = 1, no jump discontinuities, and removable discontinuities at x = 0 and x =-1. It has a vertical asymptote at x = 1. 16. Sketch omitted. The graph has a jump discontinuity at x = 1, but is con-tinuous from the left there. Otherwise, f ( x ) is continuous. 17. A ( t ) = 10(4) t 10 ; 320 grams 18. Show f ( g ( x )) = x and g ( f ( x )) = x for the x values in the proper domains; a diﬀerent way is to solve one of the functions for x and see that it is the other function....
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E1RevAns - f(1 = 3 f x is continuous from the left at 0 and...

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