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Calculus 5e_Part182

# Calculus 5e_Part182 - 362 CHAPTER 4 APPLICATIONS OF...

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1–6 |||| Find the local and absolute extreme values of the function on the given interval. 1. 2. 3. , 4. , 5. , 6. , 7–14 |||| Evaluate the limit. 7. 8. 9. 10. 11. 12. 13. 14. 15–17 |||| Sketch the graph of a function that satisﬁes the given conditions. 15. , on , and on and on and on and 16. , is continuous and even, if if , if 17. is odd, for , for , for , for , 18. The ﬁgure shows the graph of the derivative of a function . (a) On what intervals is increasing or decreasing? (b) For what values of does have a local maximum or minimum? f x f f f ± lim x l ² f ± x ² ± ³ 2 x ´ 3 f µ ± x ² 0 0 x 3 f µ ± x ² ´ 0 x ´ 2 f ± ± x ² ´ 0 0 x 2 f ± ± x ² 0 f x ´ 3 f ± ± x ² ± 1 1 x 3 0 x 1, f ± ± x ² ± ³ 1 f ± ± x ² ± 2 x f f ± 0 ² ± 0 ± 6, 12 ² ± 0, 6 ² f µ ± x ² 0 ± 12, ² ² , ± ³² , 0 ² f µ ± x ² ´ 0 ± 6, 9 ² , ± ³ 2, 1 ² f ± ± x ² ´ 0 ± 9, ² ² , ± ³² , ³ 2 ² , ± 1, 6 ² f ± ± x ² 0 lim x l ² f ± x ² ± 0, lim x l 6 f ± x ² ± ³² , f ± 0 ² ± 0, f ± ± ³ 2 ² ± f ± ± 1 ² ± f ± ± 9 ² ± 0 lim x l ± · ³ 2 ² ³ ± tan x ² cos x lim x l 1 ¸ ´ x x ³ 1 ³ 1 ln x µ lim x l 0 ¸ x 2 ln x lim x l ² x 3 e ³ x lim x l ² e 4 x ³ 1 ³ 4 x x 2 lim x l 0 e 4 x ³ 1 ³ 4 x x 2 lim x l 0 1 ³ cos x x 2 ¸ x lim x l 0 tan x ln ± 1 ¸ x ² 1, 3 · f ± x ² ± ± ln x ²³ x 2 0, · f ± x ² ± x ¸ sin 2 x ³ 2, 1 · f ± x ² ± ± x 2 ¸ 2 x ² 3 ³ 2, 0 · f ± x ² ± x x 2 ¸ x ¸ 1 f ± x ² ± x ³ s x , 0, 4 · f ± x ² ± 10 ¸ 27 x ³ x 3 , 0, 4 · 362 ❙❙❙❙ CHAPTER 4 APPLICATIONS OF DIFFERENTIATION (c) Sketch the graph of . (d) Sketch a possible graph of . 19–34 |||| Use the guidelines of Section 4.5 to sketch the curve. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. ; 35–38 |||| Produce graphs of that reveal all the important aspects of the curve. Use graphs of and to estimate the intervals of increase and decrease, extreme values, intervals of concavity, and inﬂection points. In Exercise 35 use calculus to ﬁnd these quantities exactly.

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Calculus 5e_Part182 - 362 CHAPTER 4 APPLICATIONS OF...

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