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23. lim (1 + x)cotx

23. lim (1 + x)cotx

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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7.6 L In (3x + 5) ex/1000 13. lim xo In (7x + 3) + 1 14. lim x 3e3* + 5 which functi x² - In (2/x) In (3x + 5e*) a. In 16. lim x In (7x + 3e2x) 15. lim 3x2 + 2x use с. х* 2* onimos 18. lim T 50-53. Li of the pare et of In x. 17. lim x0 x + 1 .2 29-40< 19-28. 1°, 0°, oº forms Evaluate the following limits or explain why they do not exist. Check your results by graphing. case, grap your resu 50. lim 19. lim (1 + 2x)3/x 20. lim (1 + 4x)3/x 21. lim (tan 0)cosemol Dai 22. lim (sin 0)tan e 52. lim 0→n/2 ly In x 23. lim (1 + x)cotx 24. lim 1 + 54. Ave 10)? ,2)mo 25. - om lim (tan x)* 26. lim 1 + a. b. 27. lim (x + cos x)'/x 28. lim ( 3* + 2*)/x aley 29-40. Comparing growth rates Use limit methods to determine which of the two given functions grows faster, or state that they have comparable growth rates. 0. 40< des с. 1 the 29. x10. е0.01х 30. x2 In x; In?x 31. In x20; In x 32. In x; In (In x) 33. 100%; х* 34. x2 In x; x³ d. 35. x20, 1.00001* 36. x10 In10 x: x!l 37. x*; (x/2)* AR 38. In Vr; In? 39. e. e10x 40. e: x*/10 Appli Further Explorations 41. Explain why or why not Determine whether the following state- ments are true and give an explanation or counterexample. 55. C sa а. a. lim x is an indeterminate form. b. The number 1 raised to any fixed power is 1. Therefore, be- b.
Transcribed Image Text:7.6 L In (3x + 5) ex/1000 13. lim xo In (7x + 3) + 1 14. lim x 3e3* + 5 which functi x² - In (2/x) In (3x + 5e*) a. In 16. lim x In (7x + 3e2x) 15. lim 3x2 + 2x use с. х* 2* onimos 18. lim T 50-53. Li of the pare et of In x. 17. lim x0 x + 1 .2 29-40< 19-28. 1°, 0°, oº forms Evaluate the following limits or explain why they do not exist. Check your results by graphing. case, grap your resu 50. lim 19. lim (1 + 2x)3/x 20. lim (1 + 4x)3/x 21. lim (tan 0)cosemol Dai 22. lim (sin 0)tan e 52. lim 0→n/2 ly In x 23. lim (1 + x)cotx 24. lim 1 + 54. Ave 10)? ,2)mo 25. - om lim (tan x)* 26. lim 1 + a. b. 27. lim (x + cos x)'/x 28. lim ( 3* + 2*)/x aley 29-40. Comparing growth rates Use limit methods to determine which of the two given functions grows faster, or state that they have comparable growth rates. 0. 40< des с. 1 the 29. x10. е0.01х 30. x2 In x; In?x 31. In x20; In x 32. In x; In (In x) 33. 100%; х* 34. x2 In x; x³ d. 35. x20, 1.00001* 36. x10 In10 x: x!l 37. x*; (x/2)* AR 38. In Vr; In? 39. e. e10x 40. e: x*/10 Appli Further Explorations 41. Explain why or why not Determine whether the following state- ments are true and give an explanation or counterexample. 55. C sa а. a. lim x is an indeterminate form. b. The number 1 raised to any fixed power is 1. Therefore, be- b.
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