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calculus1-1

# Thomas' Calculus, Early Transcendentals, Media Upgrade (11th Edition)

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CHAPTER 1 FUNCTIONS 1.1 FUNCTIONS AND THEIR GRAPHS 1. domain ( ); range [1 ) 2. domain [0 ); range ( 1] œ _ß _ œ ß _ œ ß _ œ 3. domain ( ); y in range y , t 0 y and y y can be any positive real number œ !ß _ Ê œ Ê œ ! Ê " " # È t t range ( ). Ê œ !ß _ 4. domain [0 ); y in range y , t 0. If t 0, then y 1 and as t increases, y becomes a smaller œ ß _ Ê œ œ œ " 1 t È and smaller positive real number range (0 1]. Ê œ ß 5. 4 z (2 z)(2 z) 0 z [ 2 2] domain. Largest value is g(0) 4 2 and smallest value is œ   Í ß œ œ œ # È g( 2) g(2) 0 0 range [0 2]. œ œ œ Ê œ ß È 6. domain ( 2 2) from Exercise 5; smallest value is g(0) and as 0 z increases to 2, g(z) gets larger and œ ß œ " # larger (also true as z 0 decreases to 2) range . Ê œ ß _ " # 7. (a) Not the graph of a function of x since it fails the vertical line test. (b) Is the graph of a function of x since any vertical line intersects the graph at most once. 8. (a) Not the graph of a function of x since it fails the vertical line test. (b) Not the graph of a function of x since it fails the vertical line test. 9. y x 1 and x . So, œ " Ê "   ! Ê Ÿ ! É ˆ ‰ " " x x (a) No (x ; (b) No; division by undefined; ! (c) No; if x , ; (d)   " " Ê " ! Ð!ß "Ó " " x x 10. y x x x and x . x x and x x So, x . œ # Ê #   ! Ê   ! Ÿ #   ! Ê   ! Ÿ # Ê Ÿ %Þ ! Ÿ Ÿ % É È È È È È È (a) No; (b) No; (c) Ò!ß %Ó 11. base x; (height) x height x; area is a(x) (base)(height) (x) x x ; œ œ Ê œ œ œ œ # # # # # # # # # " " ˆ ‰ Š x 3 3 3 4 È È È perimeter is p(x) x x x 3x. œ œ 12. s side length s s d s ; and area is a s a d œ Ê œ Ê œ œ Ê œ # # # # # " # d 2 È 13. Let D diagonal of a face of the cube and the length of an edge. Then D d and œ j œ j œ # # # D 2 3 d . The surface area is 6 2d and the volume is . # # # # # # \$ \$Î# œ j Ê j œ Ê j œ j œ œ j œ œ d 6d d d 3 3 3 3 3 È È Š 14. The coordinates of P are x x so the slope of the line joining P to the origin is m (x 0). Thus, ˆ È ß œ œ È È x x x " x, x , .

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calculus1-1 - CHAPTER 1 FUNCTIONS 1.1 FUNCTIONS AND THEIR...

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