Calc1 Flashcards
sequence
1
limit of sequence
2
sequence convergence
3
defn, divergent, two types
monotonic
4
bounded
5
convergent sequence properties
6
10 of em
limits of functions
7
defn, below, above, limit
properties of limits of functions
8
5 of em
limit of functions as x→±∞
9
special limits
10
4 general ones, 4 for a > 1, 4 for 0
f continuous at a
11
properties of continuous functions
12
3 continuous everywhere, 3 continuous where they’re defined, 4 properties, chain rule
extreme value theorem
13
Bolzano’s theorem
14
f(c)=0
intermediate value theorem
15
Brouwer’s fixed-point theorem
16
derivative
17
defn, tangent line, continuity
derivative properties
18
6 of em
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
implicit differentiation
20
higher order derivatives
21
properties of the first derivative
22
f’(x) ,= 0
critical point of f
23
properties of the second derivative
24
inflection point
25
local minimum/maximum
26
nth derivative test
27
absolute minimum/maximum
28
extremum
29
Rolle’s theorem
30
f’(c)=0
mean-value theorem for derivatives
31
related rates
32
indefinite integral
33
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)
integration by substitution
35
ex. x^2(x^3+4)^5
integration by parts
36
ex. x*logx
trig substitutions
37
3 substitutions
method of partial fractions
38
ex. 1/(x^4-x^2)
definite integral
39
Riemann sum
40
properties of definite integral
41
6 of em
fundamental theorem of calculus
42
2 parts
mean-value theorem for integrals
43
area between two curves
44
cartesian coordinates
45
polar coordinates
46
conversions of cartesian to polar
47
derivative of polar coordinates
48
area enclosed by polar equation
49
arc length for polar coordinates
50
solid of revolution
51
volume of the solid of revolution
52
formula for arc length
53
formula for surface area, 1D
54 function rotated about x or y axis
calculating the center of mass
55
exponential e
56
natural exponential / logarithm functions
57
defn, defn, property
indeterminate form
58
L’Hôpital’s rule
59
improper integrals
60
improper integral kinds
61
infinite series
62
partial sums
63
convergence of infinite series
64
defn
geometric series
65
harmonic series
66
convergence tests for infinite series
67
3 of em
p-series
68
comparison test / limit comparison test
69
ratio test
70
root test
71
integral test
72
alternating series
73
alternating series test
74
absolute convergence
75
converges absolutely, converges conditionally, thrm
power series
76
radius of convergence of a power series
77
function defined by a power series
78
properties of functions defined by power sereis
79
3 of em
Taylor series
80
common Taylor series
81
1/(1-x), 1/(1+x), log(1+x), e^x, sinx, cosx
Taylor polynomial
82
defn, error
series in powers of (x-a)
83
series, Taylor coefficients, error
parametric equations, derivatve
84
parametric equations, area under the curve
85
parametric equations, arc length
86
