Calc BC Cram Session!!!

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69 Terms

1
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Average value of a function f(x)

1/(b-a) * ∫ f(x) dx from a to b

2
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Average rate of change of f(x) from a to b

f(b) - f(a) / b-a

3
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Polar to rectangular coordinates: x=?

rcosθ

4
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Polar to rectangular coordinates: y=?

rsinθ

5
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Rectangular to polar coordinates: r=?

v(x²+y²)

6
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Rectangular to polar coordinates: θ=?

arctan(y/x)

7
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Area of a sector of a circle

½θr²

8
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Area of a region defined by a polar function

½∫r²dθ from θ1 to θ2

9
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Area between two polar curves

½ ∫router curve²-rinner curve²dθ from θ1 to θ2

10
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term image
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11
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Displacement of f(x)

∫f’(x)dx from a to b

12
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Distance of f(x)

∫|f’(x)|dx from a to b

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Speed of f(x)

|f’(x)|

14
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Arclength of f(x)

∫v(1+[f’(x)]²)dx from a to b

15
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Displacement of ⟨x(t), y(t)

<p></p>
16
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Distance of ⟨x(t), y(t)

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17
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Speed of ⟨x(t), y(t)

v((x’(t))²+(y’(t))²)

<p>v((x’(t))²+(y’(t))²)</p>
18
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Arc length of ⟨x(t), y(t)⟩

knowt flashcard image
19
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∫x^a dx

[x^(a+1)] / (a+1) + c

20
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∫e^x dx

e^x + c

21
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∫lnx dx

xlnx - x + c

22
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∫cosx dx

sinx + c

23
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∫secxtanx dx

secx + c

24
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∫csc²x dx

-cotx + c

25
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∫secx dx

ln|secx + tanx| + c

26
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∫cscx dx

ln|cscx - cotx| + c

27
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∫1/(a²+x²) dx

1/a arctan(x/a) + c

28
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∫1/x dx

ln|x| + c

29
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∫a^x dx

a^x/lna + c

30
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∫sinx dx

-cos(x) + c

31
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∫sec²x dx

tanx + c

32
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∫cscxcotx dx

-cscx + c

33
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∫tanx dx

ln|secx| + c

34
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∫cotx dx

ln|sinx| + c

35
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∫1/v(a²-x²) dx

arcsin(x/a) + c

36
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∫1/xv(x²-a²) dx

1/a * arcsec(x/a) + c

37
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In the exponential model y=Ce^(Kx), what is y?

Final amount

38
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In the exponential model y=Ce^(Kx), what is C?

Initial amount

39
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In the exponential model y=Ce^(Kx), what is K?

Growth/decay constant

40
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In the exponential model y=Ce^(kx), what is x?

Time

41
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In the logistic model y = a/(1+be^(-aKt)), what is a?

Carrying capacity

42
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What does a geometric series look like?

knowt flashcard image
43
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When does a geometric series diverge?

When |r| ≥ 1

44
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How do you find the sum that a geometric series converges to?

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45
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Using the N-th term test, when does a series diverge?

If the limit as n approaches infinity of an does not equal 0

46
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What are the criteria for f(x) in the integral test for convergence?

f(x) must be positive, continuous, and decreasing

47
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When does a series converge according to the p series test?

When p>1

48
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When does a series diverge according to the p series test

When 0<p≤1

49
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What is it called when p=1 in a p series?

Harmonic series

50
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What does a p series look like?

knowt flashcard image
51
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What is the first condition for an alternating series to converge?

The limit as n approaches infinity of an = 0

52
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What is the second condition for an alternation series to converge?

an+1 ≤ an (an are non-increasing)

53
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How is the error for an estimate of an alternating series found?

error ≤ |an+1|

54
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sinx’ = ?

cosx

55
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cosx’ = ?

-sinx

56
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tanx’ = ?

sec²x

57
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secx’ = ?

secxtanx

58
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cotx’ = ?

-csc²x

59
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cscx’ = ?

-cscxcotx

60
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arcsinx’ = ?

1/v(1-x²)

61
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arccosx’ = ?

-1/v(1-x²)

62
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arctan’ = ?

1/(1+x²)

63
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arccotx’ = ?

-1/(1+x²)

64
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arcsecx’ = ?

1/(|x|v(x²-1))

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arccscx’

-1/(|x|v(x²-1))

66
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lnx’ = ?

1/x

67
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logax’ = ?

1/xlna

68
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ex’ = ?

ex

69
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ax’ = ?

axlna