things to know Flashcards
(75 cards)
1
Q
lim sinx/ x =
x-> 0
A
1
2
Q
lim cos(x-1) /x = x-> 0
A
0
3
Q
product rule
A
U’V + V’U = d’UV
4
Q
quotient rule
A
d’U/V = (U’V - V’U)/V^2
5
Q
d’ sinx=
A
cosx
6
Q
d’ cos x
A
-sinx
7
Q
d’ tanx
A
sec^2 (x)
8
Q
what is sec
A
1/cos
9
Q
what is csc
A
1/sin
10
Q
d’ ln (x)
A
1/x
11
Q
log (base A) x
A
lnx/lna
12
Q
d’log (base A) x
A
1/uln A (du)
13
Q
d’ A^u
A
a^u (ln A) du/dx
14
Q
ln A + ln B =
A
Ln AB
15
Q
ln A - Ln B
A
ln A/B
16
Q
Ln A^B
A
Bln A
17
Q
integral of Sin ax
A
- cos ax / a
18
Q
integral of cos ax
A
sin ax /a
19
Q
integral of secant ax tan ax
A
sec ax /a
20
Q
integral of sec^2 ax
A
tan ax / a
21
Q
integral of csc ax cotax
A
-csc ax /a
22
Q
integral of csc^2 ax
A
-cot ax /a
23
Q
average value theorem
A
1/ (b-a) integral from a to b f(x)
24
Q
integral of du/u
A
ln |u|
25
integral of e^kx
1/k e^kx
26
integration by parts formula
uv- integral v du
27
derivative of inverse sin
1/ squareroot (1-u^2)
28
derivative of inverse cos
-1/ squareroot (1-u^2)
29
1/ squareroot (1-u^2)
derivative of inverse sin
30
-1/ squareroot (1-u^2)
derivative of inverse cos
31
derivative of inverse tan
1/ (1+ u^2)
32
1/ (1+ u^2)
derivative of inverse tan
33
derivative of inverse cotan
-1/ (1+ u^2)
34
-1/ (1+ u^2)
derivative of inverse cotan
35
derivative of inverse secant
1/ (squareroot (u^2-1)) (|u|)
36
1/ (squareroot (u^2-1)) (|u|)
derivative of inverse secant
37
derivative of inverse cosecant
-1/ (squareroot (u^2-1)) (|u|)
38
-1/ (squareroot (u^2-1)) (|u|)
derivative of inverse cosecant
39
integral of tanx
-ln |cosx|
40
integral of secx
-ln |secx+ tanx|
41
integral of csc^2 (x)
-cotx
42
integral of csc cot
-csc
43
integral of cot
ln |sinx|
44
integral of csc
-ln |csc+cot|
45
length of a curve
integral of squareroot of (1 + (dy/dx)^2)
46
parametric funcion curve length
integral of squarroot of dx^2 + dy^2
47
area of polar cordinates
integral of 1/2 r^2 d theta
48
eulors method
x plus step for new x
y plus old slope times step for new y
plug into exuation for new slope
49
sum of first n terms of geometric series
= a(1-r^n)
---------------
(1-r)
50
sum of infinite geometric series
a
----
1-r
51
ratio test
Lim A(n+ 1
_____
an
P less that 1 converges
P greater that 1 divergest
= 1 insufficient info
52
alternating series
1. decresing
2. alternating
3. limit to infinity is 0
53
Integral test
Integral from 1 to infinity of fx
54
e^x power series
1+ x +x^2/2! +x^3/3!
55
Sin x power series
X- x^3/3!+x^5/5!-x^7/7!
56
Cos x power series
1 - x^2/2! + x^4/4! -x^6/6!
57
Ln(1+x) power series
X- x^2/2+x^3/3
58
pi= how many degrees
180
59
pi/4
45
60
pi/2
90
61
pi/3
60
62
pi/6
30
63
180 degrees in radian
pi
64
45 degrees in radian
pi/4
65
90 degrees in radian
pi/2
66
60 degrees in radian
pi/3
67
30 degrees in radian
pi/6
68
sin pi/6
1/2
69
sin pi/4
square root 2 over 2
70
sin pi/3
squareroot 3 over 2
71
sin 90
1
72
cos pi/6
squareroot 3 over 2
73
cos pi/4
square root 2 over 2
74
cos pi/3
1/2
75
cos pi/2
0
