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 ß _ œ ß ± _ ß 3. domain ( ); y in range y , t 0 y and y y can be any positive real number œ! ß_ Ê œ ² Ê œ ²!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 œß_ ² œ œ " ± 1t È and smaller positive real number range (0 1]. Êœ 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± ³ Í−± ßœ œ œ # È g( 2) g(2) 0 0 range [0 2]. ±œ œ œ Ê œß 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 ²! É ˆ‰ xx (a) No (x ; (b) No; division by undefined; ²!Ñ ! (c) No; if x , ; (d)  " ´"Ê ±"´! Ð! ß" Ó 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 ÈÈÈ 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 ; œ³ œ Ê œ œ œ œ ## # # # # # Š‹ x 33 3 4 ÈÈ È perimeter is p(x) x x x 3x. œ³³œ 12. s side length s s d s ; and area is a s a d œÊ ³ 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 œj œ j ³ œ ### D 2 3 . The surface area is 6 2d and the volume is . # # # # \$ \$Î# œjÊ jœ Êjœ jœ œ œ d6 d d d 3 È È \$ 14. The coordinates of P are x x so the slope of the line joining P to the origin is m (x 0). Thus, È œ ² È È x x x " x, x , . È œ mm #

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2 Chapter 1 Functions 15. The domain is . 16. The domain is .
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calculus1-1 - CHAPTER 1 FUNCTIONS 1.1 FUNCTIONS AND THEIR...

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