Calc1

Question 1

sequence

Answer 1

1

Question 2

limit of sequence

Answer 2

2

Question 3

sequence convergence

Answer 3

3

defn, divergent, two types

Question 4

monotonic

Answer 4

4

Question 5

bounded

Answer 5

5

Question 6

convergent sequence properties

Answer 6

6

10 of em

Question 7

limits of functions

Answer 7

7

defn, below, above, limit

Question 8

properties of limits of functions

Answer 8

8

5 of em

Question 9

limit of functions as x→±∞

Answer 9

9

Question 10

special limits

Answer 10

10

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

Question 11

f continuous at a

Answer 11

11

Question 12

properties of continuous functions

Answer 12

12

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

Question 13

extreme value theorem

Answer 13

13

Question 14

Bolzano’s theorem

Answer 14

14

f(c)=0

Question 15

intermediate value theorem

Answer 15

15

Question 16

Brouwer’s fixed-point theorem

Answer 16

16

Question 17

derivative

Answer 17

17

defn, tangent line, continuity

Question 18

derivative properties

Answer 18

18

6 of em

Question 19

common derivatives

Answer 19

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

Question 20

implicit differentiation

Answer 20

20

Question 21

higher order derivatives

Answer 21

21

Question 22

properties of the first derivative

Answer 22

22

f’(x) ,= 0

Question 23

critical point of f

Answer 23

23

Question 24

properties of the second derivative

Answer 24

24

Question 25

inflection point

Answer 25

25

Question 26

local minimum/maximum

Answer 26

26

Question 27

nth derivative test

Answer 27

27

Question 28

absolute minimum/maximum

Answer 28

28

Question 29

extremum

Answer 29

29

Question 30

Rolle's theorem

Answer 30

30 | f'(c)=0

Question 31

mean-value theorem for derivatives

Answer 31

31

Question 32

related rates

Answer 32

32

Question 33

indefinite integral

Answer 33

33

Question 34

common integrals

Answer 34

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)

Question 35

integration by substitution

Answer 35

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

Question 36

integration by parts

Answer 36

36 | ex. x*logx

Question 37

trig substitutions

Answer 37

37 | 3 substitutions

Question 38

method of partial fractions

Answer 38

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

Question 39

definite integral

Answer 39

39

Question 40

Riemann sum

Answer 40

40

Question 41

properties of definite integral

Answer 41

41 | 6 of em

Question 42

fundamental theorem of calculus

Answer 42

42 | 2 parts

Question 43

mean-value theorem for integrals

Answer 43

43

Question 44

area between two curves

Answer 44

44

Question 45

cartesian coordinates

Answer 45

45

Question 46

polar coordinates

Answer 46

46

Question 47

conversions of cartesian to polar

Answer 47

47

Question 48

derivative of polar coordinates

Answer 48

48

Question 49

area enclosed by polar equation

Answer 49

49

Question 50

arc length for polar coordinates

Answer 50

50

Question 51

solid of revolution

Answer 51

51

Question 52

volume of the solid of revolution

Answer 52

52

Question 53

formula for arc length

Answer 53

53

Question 54

formula for surface area, 1D

Answer 54

``` 54 function rotated about x or y axis ```

Question 55

calculating the center of mass

Answer 55

55

Question 56

exponential e

Answer 56

56

Question 57

natural exponential / logarithm functions

Answer 57

57 | defn, defn, property

Question 58

indeterminate form

Answer 58

58

Question 59

L'Hôpital's rule

Answer 59

59

Question 60

improper integrals

Answer 60

60

Question 61

improper integral kinds

Answer 61

61

Question 62

infinite series

Answer 62

62

Question 63

partial sums

Answer 63

63

Question 64

convergence of infinite series

Answer 64

64 | defn

Question 65

geometric series

Answer 65

65

Question 66

harmonic series

Answer 66

66

Question 67

convergence tests for infinite series

Answer 67

67 | 3 of em

Question 68

p-series

Answer 68

68

Question 69

comparison test / limit comparison test

Answer 69

69

Question 70

ratio test

Answer 70

70

Question 71

root test

Answer 71

71

Question 72

integral test

Answer 72

72

Question 73

alternating series

Answer 73

73

Question 74

alternating series test

Answer 74

74

Question 75

absolute convergence

Answer 75

75 | converges absolutely, converges conditionally, thrm

Question 76

power series

Answer 76

76

Question 77

radius of convergence of a power series

Answer 77

77

Question 78

function defined by a power series

Answer 78

78

Question 79

properties of functions defined by power sereis

Answer 79

79 | 3 of em

Question 80

Taylor series

Answer 80

80

Question 81

common Taylor series

Answer 81

81 | 1/(1-x), 1/(1+x), log(1+x), e^x, sinx, cosx

Question 82

Taylor polynomial

Answer 82

82 | defn, error

Question 83

series in powers of (x-a)

Answer 83

83 | series, Taylor coefficients, error

Question 84

parametric equations, derivatve

Answer 84

84

Question 85

parametric equations, area under the curve

Answer 85

85

Question 86

parametric equations, arc length

Answer 86

86