Flashcards in Calc1 Deck (86):

1

## sequence

### 1

2

## limit of sequence

### 2

3

## sequence convergence

###
3

defn, divergent, two types

4

## monotonic

### 4

5

## bounded

### 5

6

## convergent sequence properties

###
6

10 of em

7

## limits of functions

###
7

defn, below, above, limit

8

## properties of limits of functions

###
8

5 of em

9

## limit of functions as x→±∞

### 9

10

## special limits

###
10

4 general ones, 4 for a > 1, 4 for 0

11

## f continuous at a

### 11

12

## properties of continuous functions

###
12

3 continuous everywhere, 3 continuous where they're defined, 4 properties, chain rule

13

## extreme value theorem

### 13

14

## Bolzano's theorem

###
14

f(c)=0

15

## intermediate value theorem

### 15

16

## Brouwer's fixed-point theorem

### 16

17

## derivative

###
17

defn, tangent line, continuity

18

## derivative properties

###
18

6 of em

19

## common derivatives

###
19

22 of em: k, x^k, e^x, a^x, logx, log_ax, log_a|x|, sin, cos, tan, cot, sec, csc, asin, acos, atan, csc^-1, sec^-1, cot^-1, sinh, cosh, tanh

20

## implicit differentiation

### 20

21

## higher order derivatives

### 21

22

## properties of the first derivative

###
22

f'(x) ,= 0

23

## critical point of f

### 23

24

## properties of the second derivative

### 24

25

## inflection point

### 25

26

## local minimum/maximum

### 26

27

## nth derivative test

### 27

28

## absolute minimum/maximum

### 28

29

## extremum

### 29

30

## Rolle's theorem

###
30

f'(c)=0

31

## mean-value theorem for derivatives

### 31

32

## related rates

### 32

33

## indefinite integral

### 33

34

## common integrals

###
34

k, x^k, 1/x, 1/(x-a), 1/(x^2+a^2), x/(x^2+a^2), e^(ax), a^x, sin(ax), cos(ax), sec^2(x), csc^2(x), secx tanx, cscx cotx, 1/sqrt(1-x^2), 1/(1+x^2)

35

## integration by substitution

###
35

ex. x^2(x^3+4)^5

36

## integration by parts

###
36

ex. x*logx

37

## trig substitutions

###
37

3 substitutions

38

## method of partial fractions

###
38

ex. 1/(x^4-x^2)

39

## definite integral

### 39

40

## Riemann sum

### 40

41

## properties of definite integral

###
41

6 of em

42

## fundamental theorem of calculus

###
42

2 parts

43

## mean-value theorem for integrals

### 43

44

## area between two curves

### 44

45

## cartesian coordinates

### 45

46

## polar coordinates

### 46

47

## conversions of cartesian to polar

### 47

48

## derivative of polar coordinates

### 48

49

## area enclosed by polar equation

### 49

50

## arc length for polar coordinates

### 50

51

## solid of revolution

### 51

52

## volume of the solid of revolution

### 52

53

## formula for arc length

### 53

54

## formula for surface area, 1D

###
54

function rotated about x or y axis

55

## calculating the center of mass

### 55

56

## exponential e

### 56

57

## natural exponential / logarithm functions

###
57

defn, defn, property

58

## indeterminate form

### 58

59

## L'Hôpital's rule

### 59

60

## improper integrals

### 60

61

## improper integral kinds

### 61

62

## infinite series

### 62

63

## partial sums

### 63

64

## convergence of infinite series

###
64

defn

65

## geometric series

### 65

66

## harmonic series

### 66

67

## convergence tests for infinite series

###
67

3 of em

68

## p-series

### 68

69

## comparison test / limit comparison test

### 69

70

## ratio test

### 70

71

## root test

### 71

72

## integral test

### 72

73

## alternating series

### 73

74

## alternating series test

### 74

75

## absolute convergence

###
75

converges absolutely, converges conditionally, thrm

76

## power series

### 76

77

## radius of convergence of a power series

### 77

78

## function defined by a power series

### 78

79

## properties of functions defined by power sereis

###
79

3 of em

80

## Taylor series

### 80

81

## common Taylor series

###
81

1/(1-x), 1/(1+x), log(1+x), e^x, sinx, cosx

82

## Taylor polynomial

###
82

defn, error

83

## series in powers of (x-a)

###
83

series, Taylor coefficients, error

84

## parametric equations, derivatve

### 84

85

## parametric equations, area under the curve

### 85

86