calculus1-aa

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

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Chapter 1 Practice Exercises 43 5. 6. Symmetric about the origin. Symmetric about the y-axis. 7. 8. Neither Symmetric about the y-axis. 9. y x x x y x . Even. abab a b ±œ± ² " œ ² " œ # # 10. y x x x x x x x y x . Odd. abab ab ab a b ± œ ±± ± œ ± ²² œ ± &$ 11. y x cos x cos x y x . Even. ab a b ±œ " ± ±œ " ± œ 12. y x sec x tan x sec x tan x y x . Odd. a b ± œ ± œ œ± sin x cos x cos x sin x ± ± ± ## 13. y x y x . Odd. a b œ œ ± œ ± ab ab ±² " # ± ²" ²" # ± # x xx % $ %% $$ 14. y x sin x sin x. Neither even nor odd. " " ² 15. y x x cos x x cos x. Neither even nor odd. ±² ±œ 16. y x x x y x . Even. a b É È ±œ ± ± " œ ± " œ % % 17. (a) The function is defined for all values of x, so the domain is . ±_ß _ (b) Since x attains all nonnegative values, the range is . l l Ò±#ß _Ñ 18. (a) Since the square root requires x , the domain is . " ±   ! б_ß "Ó (b) Since x attains all nonnegative values, the range is . È " ± Ò±#ß _Ñ 19. (a) Since the square root requires x , the domain is . "' ±   ! Ò±%ß %Ó # (b) For values of x in the domain, x , so x . The range is . ! Ÿ "' ± Ÿ "' ! Ÿ "' ± Ÿ % Ò!ß %Ó # # È
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44 Chapter 1 Functions 20. (a) The function is defined for all values of x, so the domain is . ab ±_ß _ (b) Since attains all positive values, the range is . $" ß _ x 21. (a) The function is defined for all values of x, so the domain is . ±_ß _ (b) Since e attains all positive values, the range is . # ±$ß _ ± x 22. (a) The function is equivalent to y tan x, so we require x for odd integers k. The domain is given by x for œ# # Á Á kk 11 #% odd integers k. (b) Since the tangent function attains all values, the range is . ±_ß _ 23. (a) The function is defined for all values of x, so the domain is . ±_ß _ (b) The sine function attains values from to , so sin x and hence sin x . The ±" " ±#Ÿ# $ ² Ÿ# ±$Ÿ# ±"Ÿ" range is 3 1 . Ò± ß Ó 24. (a) The function is defined for all values of x, so the domain is . ±_ß _ (b) The function is equivalent to y x , which attains all nonnegative values. The range is . œ Ò!ß _Ñ È & # 25. (a) The logarithm requires x , so the domain is . ± $ ³ ! $ß _ (b) The logarithm attains all real values, so the range is . ±_ß _ 26. (a) The function is defined for all values of x, so the domain is . ±_ß _ (b) The cube root attains all real values, so the range is . ±_ß _ 27. (a) The function is defined for x , so the domain is . ±% Ÿ Ÿ % Ò±%ß %Ó (b) The function is equivalent to y x , x , which attains values from to for x in the domain. The œl l ± % ŸŸ % !# È range is . Ò!ß #Ó 28. (a) The function is defined for x , so the domain is . ±# Ÿ Ÿ # Ò±#ß #Ó
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calculus1-aa - Chapter 1 Practice Exercises 5. 6. 43...

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