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)
