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CHAPTER 7 MEMORY ITEMS Short Answer 1. Define the natural logarithm as an integral. . 2. dx = 3. d/dx ( ln x ) = 4. d/dx ( ln |x| ) = 5. d/dx ( ln f(x) ) = 6. ln 1 = 7. ln ab = 8. ln a/b = 9. ln a 10. What formula is used to convert log base b into a natural logarithm expression ? . 11. Explain how to take the derivative of a function written as a variable expression raised to a variable power. . 12. What is the relationship between the derivative of f at x=a y=b and the derivative of f inverse? . 13. e = 14. ln e = 15. e · e = 16. e = 17. e = 18. d/dx (e ) = 19. d/dx (e )= 20. d/dx (a )= 21. d/dx (a ) = 22. dx = 23. dx = 24. d/dx ( log x) = 25. If f ' (x) = k · f(x) then f(x) = 26. lim ( 1 + c/x ) = x oo 27. lim ( 1 + cx ) x 0 = 28. What is the equation for computing continuously compounded interest ? . 29. Give the principal domain of sin x 30. Give the principal domain of cos x 31. Give the principal domain of tan x 32. Give the principal domain of sec x 33. d/dx ( sin x ) = 34. d/dx ( cos x ) = 35. d/dx ( tan x ) = 36. d/dx ( sec x ) = 37. 1/ dx = 38. -1/ 39. 1/ 40. dx = dx = dx = CHAPTER 7 MEMORY ITEMS Answer Section SHORT ANSWER 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. dt = ln x for x>0 ln |x| + C 1/x 1/x f ' (x) / f(x) 0 ln a + ln b ln a - ln b r ln a log x = ln x / ln b 11. take the ln of both sides first, bring down the power, use implicit differentiation 12. (f ) ' (b) = 1 / f ' (a) 13. x 14. x 15. e 16. e · e 17. e / e 18. e 19. e · f ' (x) 20. a · f ' (x) · ln a 21. a ln a 22. 1/lna a + C 23. e + C 24. 1/(x lna) 25. A e 26. e 27. e 28. A = A e 29. 30. 31. 32. [- /2 , /2 ] [0, ] [- /2 , /2 ] [0, ], x /2 33. 1/ 34. -1/ 35. 36. 1/ 37. sin x + C 38. cos x + C 39. sec x + C