Chapter 5 Flashcards Preview

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Flashcards in Chapter 5 Deck (43):
1

y = logb(x) means...

b^y = x

2

What is the Common Log and what does it mean?

- y = log(x)
- y = log10(x)

3

What is the Natural Log and what does it mean?

- y = ln(x)
- y = loge(x)

4

ln (1) = ?

0

5

ln(e) = ?

1

6

ln(e^x)

x

7

e^(ln(x)) = ?

x

8

log(1) = ?

0

9

log(10) = ?

1

10

log(10^x) = ?

x

11

10^(log10(x)) = ?

x

12

logb(1) = ?

0

13

logb(b) = ?

1

14

logb(b^x) = ?

x

15

b^(logb(x)) = ?

x

16

ln(M*N) = ?

ln(M) + ln(N)

17

ln(M/N) = ?

ln(M) - ln(N)

18

ln(1/N) = ?

ln(1) - ln(N) = -ln(N)

19

ln(M^n) = ?

n*ln(M)

20

What is the domain and range of y = ln(x)?

Domain: x > 0 or (0,∞)
Range: All Real Numbers

21

What is the domain and range of e^y = x?

Domain: x > 0 or (0,∞)
Range: All Real Numbers

22

d[ln(u)] = ?

du/u

23

{du/u = ?

ln|u| + c

24

{secu * du = ?

ln|secu + tanu| + c

25

{cscu * du = ?

ln|cscu - cotu| + c

26

{sinu * du = ?

-cosu + c

27

{cosu * du = ?

sinu + c

28

{tanu * du = ? *show work for this one*

-ln|cosu| + c

29

{cotu * du = ?

ln|sinu| + c

30

d(e^u) = ?

e^u * du

31

{e^u * du = ?

e^u + c

32

d[loga(u)] = ?

1/ln(a) * (du/u)

33

d(a^u) = ?

a^u * ln(a) * du

34

{a^u * du = ?

1/ln(a) * a^u + c

35

d(arcsinu) = ?

1/(√1-u^2) * du

36

d(arccosu) = ?

-1/(√1-u^2) * du

37

d(arctanu) = ?

1/(u^2 + 1) * du

38

d(arccotu) = ?

-1/(u^2 + 1) * du

39

d(arcsecu) = ?

1/(u√u^2 -1) * du

40

d(arccscu) = ?

-1/(u√u^2 -1) * du

41

{du/√(a^2)-(u^2) = ?
*a = #, u = variable

arcsin(u/a) + c

42

{du/(a^2)+(u^2) = ?
*a = #, u = variable

(1/a) arctan(u/a) + c

43

{du/√u(u^2)-(a^2) = ?
*a = #, u = variable

(1/a) arcsec(u/a) + c