Exam 1 Flashcards
1
Q
integral of 1/x
A
ln abs value x
2
Q
integral e to the x
A
e to the x
3
Q
integral sinx
A
-cosx
4
Q
integral sec^2x
A
tanx
5
Q
integral secxtanx
A
secx
6
Q
integral secx
A
ln I secx + tanx I
7
Q
integral tanx
A
ln I secx I
8
Q
integral 1/(sq. root 1-x^2)
A
arcsinx (sin-1x)
9
Q
integral b^x
A
b^x/lnb
10
Q
integral cosx
A
sinx
11
Q
integral csc^2x
A
-cotx
12
Q
integral cscxcotx
A
-cscx
13
Q
integral cscx
A
ln I cscx-cotx I
14
Q
integral cotx
A
ln I sinx I
15
Q
integral 1/x^2 +1
A
arctanx (tan-1x)
16
Q
sin^2x + cos^2x
A
1
17
Q
tan^2x +1 =
A
sec^2x
18
Q
1 + cot^2x =
A
csc^2x
19
Q
sin2x
A
2sinxcosx
20
Q
cos2x
A
cos^2x - sin^2x
2cos^2x-1
21
Q
sin^2x =
A
1/2 (1-cos2x)
22
Q
cos^2x=
A
1/2(1+cos2x)
23
Q
tan^2x=
A
(1-cos2x)/(1+cos2x)
24
Q
volume of a sphere
A
v= 4/3 pi r^3
25
area of a pyramid or cone
v= 1/3 (area of base) height
26
volume of prism or cylinder
v= (area of base) height
27
cos (0)
1
28
cos(pi/6)
(sq root 3)/2
29
cos(pi/4)
(sq root 2)/2
30
cos(pi/3)
1/2
31
cos(pi/2)
0
32
cos pi
-1
33
sin(0)
0
34
sin(pi/6)
1/2
35
sin(pi/4)
(sq root 2)/2
36
sin(pi/3)
(sq root 3)/2
37
sin(pi/2)
1
38
sin(pi)
0
39
tan(0)
0
40
tan(pi/6)
(sq root 3)/3
41
tan(pi/4)
1
42
tan(pi/3)
sq root 3
43
tan(pi/2)
undefined
44
tan(pi)
0
45
graph y=x^2 - 2
parabola shifted down 2
46
graph y= (x-3)^2
parabola shifted to the right 3
47
trig integrals sincos
if sin power is odd use cos^2x= 1-sin^2x and make u=sinx
if cos power is odd use sin^2x= 1- cos^2x and make u=cosx
if they are both even use half angle identities
48
trig identities tansec
if sec is even, use sec^2x=1+tan^2x and make u=tanx
if tan is odd, use tan^2x=sec^2x -1 and make u=secx
49
trig sub
a2-x2 -> x=asin(theta)
a2+x2 -> x=atan(theta)
x2-a2 -> x=asec(theta)
50
integral of 1/(x^2+a^2)
1/a ⢠tan-1 (x/a) +C
51
comparison theorem
f(x)>g(x)
if f(x) is convergent then g(x) is convergent
if g(x) is divergent then f(x) is divergent
52
lim r^n
0 if -1
53
geometric series
E ar^n-1
54
geometric series sum
s=a/1-r and r<1, converges
diverges if r>or= 1
55
if lim an
doesnt exist or doesnt equal 0, divergent
56
arc length
L= integral of the sq. root (1+fâ(x)^2)
57
p-series
if p>1 convergent
| if p<1 divergent
