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