Ap Calculus Bc

Front 1

D(ln u)

Back 1

D(u) / u

Front 2

S(Du)/u

Back 2

ln |u|

Front 3

S sin u du

Back 3

-cos u

Front 4

S cos u du

Back 4

sin u

Front 5

S sec^2 u du

Back 5

tan u

Front 6

S sec^2 u du

Back 6

tan u

Front 7

S csc^2 udu

Back 7

-cot u

Front 8

S sec^2 u du

Back 8

tan u

Front 9

S csc^2 udu

Back 9

-cot u

Front 10

S sec u tan u du

Back 10

sec u

Front 11

S sec^2 u du

Back 11

tan u

Front 12

S csc^2 udu

Back 12

-cot u

Front 13

S sec u tan u du

Back 13

sec u

Front 14

S csc u cot u du

Back 14

-csc u

Front 15

S tan u du

Back 15

-ln |cos u|

Front 16

S tan u du

Back 16

ln |sec u|

Front 17

S cot u du

Back 17

ln|sin u|

Front 18

S sec u du

Back 18

ln |sec u + tan u|

Front 19

S csc u du

Back 19

ln|csc u - cot u|

Front 20

S csc u du

Back 20

ln|csc u - cot u|

Front 21

D (e^u)

Back 21

(e^u)(D u)

Front 22

S e^u

Back 22

e^u

Front 23

D(a^u)

Back 23

(a^u) ln a (D u)

Front 24

S a^u du

Back 24

(a^u) / ln a

Front 25

S e^u

Back 25

e^u

Front 26

D(a^u)

Back 26

(a^u) ln a (D u)

Front 27

S a^u du

Back 27

(a^u) / ln a

Front 28

S e^u

Back 28

e^u

Front 29

D(a^u)

Back 29

(a^u) ln a (D u)

Front 30

S a^u du

Back 30

(a^u) / ln a

Front 31

S e^u

Back 31

e^u

Front 32

D(a^u)

Back 32

(a^u) ln a (D u)

Front 33

S a^u du

Back 33

(a^u) / ln a

Front 34

logau (change of base)

Back 34

ln u / ln a

Front 35

S e^u

Back 35

e^u

Front 36

D(a^u)

Back 36

(a^u) ln a (D u)

Front 37

S a^u du

Back 37

(a^u) / ln a

Front 38

logau (change of base)

Back 38

ln u / ln a

Front 39

D (logau)

Back 39

(D u) / ( ln a * u )

Front 40

ar^(n-1)

Back 40

converge - |r|<1

diverge - |r|>_ 1

Front 41

ar^(n-1)

Back 41

converge - |r|<1

diverge - |r|>_ 1

Front 42

(An -A(n+1))

Back 42

Con - lim n->🔗 (Sn) = L

Div - lim n-> 🔗(Sn) = 🔗

Front 43

ar^(n-1)

Back 43

converge - |r|<1

diverge - |r|>_ 1

Front 44

(An -A(n+1))

Back 44

Con - lim n->🔗 (Sn) = L

Div - lim n-> 🔗(Sn) = 🔗

Front 45

1/(n^p)

Back 45

con p>1

div p_<1

Front 46

ar^(n-1)

Back 46

converge - |r|<1

diverge - |r|>_ 1

Front 47

(An -A(n+1))

Back 47

Con - lim n->🔗 (Sn) = L

Div - lim n-> 🔗(Sn) = 🔗

Front 48

1/(n^p)

Back 48

con p>1

div p_<1

Front 49

alternating series

Back 49

con - positive, decreasing, lim=0

Front 50

ar^(n-1)

Back 50

converge - |r|<1

diverge - |r|>_ 1

Front 51

(An -A(n+1))

Back 51

Con - lim n->🔗 (Sn) = L

Div - lim n-> 🔗(Sn) = 🔗

Front 52

1/(n^p)

Back 52

con p>1

div p_<1

Front 53

alternating series

Back 53

con - positive, decreasing, lim=0

Front 54

standard equation

Back 54

y-y1=m(x-x1)

Front 55

ratio/root

Back 55

converge abs - lim < 1

div abs - lim > 1

Front 56

ratio/root

Back 56

converge abs - lim < 1

div abs - lim > 1

Front 57

lim n -> 🔗 (An/Bn) = L

Back 57

L >_ 0 = converge

L > 0 diverge

Front 58

D(logbx)

Back 58

1/x ln b

Front 59

def. of derivative

Back 59

lim h-> 🔗 ((f(x+h)-f(x))/h)

Front 60

def. of derivative

Back 60

lim h-> 🔗 ((f(x+h)-f(x))/h)

Front 61

Disk volume

Back 61

V=🍰s[f(x)]^2 dx

Front 62

Washer Volume

Back 62

V = 🍰S { f(x)^2 - g(x)^2 } dx

Front 63

Cylindrical Shells

Back 63

V = 2🍰S x f(x) dx

Front 64

Polar for x

Back 64

x = r cos ø

Front 65

Polar for y

Back 65

y = r sinø

Front 66

Polar for y

Back 66

y = r sinø

Front 67

Polar with x, y, and r

Back 67

x^2 + y^2 = r^2

Front 68

Polar with x, y, and ø

Back 68

tanø = y/x

Front 69

Polar Area

Back 69

A = S r^2 / 2 dø

Front 70

Polar Arc Length

Back 70

Back (Definition)

Front 71

Arc Length

Back 71

Back (Definition)

Front 72

Arc Length

Back 72

Back (Definition)

Front 73

Parametric Arc Length

Back 73

Back (Definition)

Front 74

Trapezoid Rule

Back 74

(b-a)/2n [(f(x0)) + 2(f(x1))...+ 2(f(xn-1)) + f(xn))]

Front 75

Taylor Polynomial

Back 75

f(a) + f'(a)(x-a)/1! + f''(a)(x-a)^2/2!...+ f^(n) (a) (x-a)^n / n!

Front 76

Taylor Polynomial

Back 76

f(a) + f'(a)(x-a)/1! + f''(a)(x-a)^2/2!...+ f^(n) (a) (x-a)^n / n!

Front 77

MacLaurin for e^x

Back 77

Back (Definition)

Front 78

Taylor Polynomial

Back 78

f(a) + f'(a)(x-a)/1! + f''(a)(x-a)^2/2!...+ f^(n) (a) (x-a)^n / n!

Front 79

MacLaurin for e^x

Back 79

Back (Definition)

Front 80

MacLaurin for cosx

Back 80

Back (Definition)

Front 81

Taylor Polynomial

Back 81

f(a) + f'(a)(x-a)/1! + f''(a)(x-a)^2/2!...+ f^(n) (a) (x-a)^n / n!

Front 82

MacLaurin for e^x

Back 82

Back (Definition)

Front 83

MacLaurin for cosx

Back 83

Back (Definition)

Front 84

MacLaurin for sinx

Back 84

Back (Definition)

Front 85

Sum of conv. geo series

Back 85

a/(1-r)

Front 86

Sum of conv. geo series

Back 86

a/(1-r)

Front 87

LaGrange Remainder

Back 87

f{deriv n+1) (z) (x-a)^(n+1) / (n+1)!

z is between a and x

Front 88

Sum of conv. geo series

Back 88

a/(1-r)

Front 89

LaGrange Remainder

Back 89

f{deriv n+1) (z) (x-a)^(n+1) / (n+1)!

z is between a and x

Front 90

odd functions

Back 90

Back (Definition)

Front 91

Sum of conv. geo series

Back 91

a/(1-r)

Front 92

LaGrange Remainder

Back 92

f{deriv n+1) (z) (x-a)^(n+1) / (n+1)!

z is between a and x

Front 93

odd functions

Back 93

Back (Definition)

Front 94

Even functions

Back 94

Back (Definition)

Front 95

Sum of conv. geo series

Back 95

a/(1-r)

Front 96

LaGrange Remainder

Back 96

f{deriv n+1) (z) (x-a)^(n+1) / (n+1)!

z is between a and x

Front 97

odd functions

Back 97

Back (Definition)

Front 98

Even functions

Back 98

Back (Definition)

Front 99

relationship between tan and sec

Back 99

Back (Definition)

Front 100

Sum of conv. geo series

Back 100

a/(1-r)

Front 101

LaGrange Remainder

Back 101

f{deriv n+1) (z) (x-a)^(n+1) / (n+1)!

z is between a and x

Front 102

odd functions

Back 102

Back (Definition)

Front 103

Even functions

Back 103

Back (Definition)

Front 104

relationship between tan and sec

Back 104

Back (Definition)

Front 105

relationship between sin and cos

Back 105

Back (Definition)

Front 106

relationship between cot and csc

Back 106

Back (Definition)

Front 107

relationship between cot and csc

Back 107

Back (Definition)

Front 108

sin2ø

Back 108

Back (Definition)

Front 109

half angle stuff

Back 109

Back (Definition)

Front 110

relationship between cot and csc

Back 110

Back (Definition)

Front 111

sin2ø

Back 111

Back (Definition)

Front 112

half angle stuff

Back 112

Back (Definition)

Front 113

relationship between cot and csc

Back 113

Back (Definition)

Front 114

sin2ø

Back 114

Back (Definition)

Front 115

half angle stuff

Back 115

Back (Definition)

Front 116

half angle stuff

Back 116

Back (Definition)

Front 117

relationship between cot and csc

Back 117

Back (Definition)

Front 118

sin2ø

Back 118

Back (Definition)

Front 119

half angle stuff

Back 119

Back (Definition)

Front 120

half angle stuff

Back 120

Back (Definition)

Front 121

trig identity sec

Back 121

Back (Definition)

Front 122

relationship between cot and csc

Back 122

Back (Definition)

Front 123

sin2ø

Back 123

Back (Definition)

Front 124

half angle stuff

Back 124

Back (Definition)

Front 125

half angle stuff

Back 125

Back (Definition)

Front 126

trig identity sec

Back 126

Back (Definition)

Front 127

integration by parts

Back 127

Back (Definition)

Front 128

relationship between cot and csc

Back 128

Back (Definition)

Front 129

sin2ø

Back 129

Back (Definition)

Front 130

half angle stuff

Back 130

Back (Definition)

Front 131

half angle stuff

Back 131

Back (Definition)

Front 132

trig identity sec

Back 132

Back (Definition)

Front 133

integration by parts

Back 133

Back (Definition)

Front 134

trig sub sin

Back 134

Back (Definition)

Front 135

relationship between cot and csc

Back 135

Back (Definition)

Front 136

sin2ø

Back 136

Back (Definition)

Front 137

half angle stuff

Back 137

Back (Definition)

Front 138

half angle stuff

Back 138

Back (Definition)

Front 139

trig identity sec

Back 139

Back (Definition)

Front 140

integration by parts

Back 140

Back (Definition)

Front 141

trig sub sin

Back 141

Back (Definition)

Front 142

trig sub tan

Back 142

Back (Definition)

Front 143

relationship between cot and csc

Back 143

Back (Definition)

Front 144

sin2ø

Back 144

Back (Definition)

Front 145

half angle stuff

Back 145

Back (Definition)

Front 146

half angle stuff

Back 146

Back (Definition)

Front 147

trig identity sec

Back 147

Back (Definition)

Front 148

integration by parts

Back 148

Back (Definition)

Front 149

trig sub sin

Back 149

Back (Definition)

Front 150

trig sub tan

Back 150

Back (Definition)

Front 151

mean value theorem

Back 151

Back (Definition)

Front 152

relationship between cot and csc

Back 152

Back (Definition)

Front 153

sin2ø

Back 153

Back (Definition)

Front 154

half angle stuff

Back 154

Back (Definition)

Front 155

half angle stuff

Back 155

Back (Definition)

Front 156

trig identity sec

Back 156

Back (Definition)

Front 157

integration by parts

Back 157

Back (Definition)

Front 158

trig sub sin

Back 158

Back (Definition)

Front 159

trig sub tan

Back 159

Back (Definition)

Front 160

mean value theorem

Back 160

Back (Definition)

Front 161

average value

Back 161

Back (Definition)

Front 162

relationship between cot and csc

Back 162

Back (Definition)

Front 163

sin2ø

Back 163

Back (Definition)

Front 164

half angle stuff

Back 164

Back (Definition)

Front 165

half angle stuff

Back 165

Back (Definition)

Front 166

trig identity sec

Back 166

Back (Definition)

Front 167

integration by parts

Back 167

Back (Definition)

Front 168

trig sub sin

Back 168

Back (Definition)

Front 169

trig sub tan

Back 169

Back (Definition)

Front 170

mean value theorem

Back 170

Back (Definition)

Front 171

average value

Back 171

Back (Definition)

Front 172

D (sec^ -1 x)

Back 172

Back (Definition)

Front 173

relationship between cot and csc

Back 173

Back (Definition)

Front 174

sin2ø

Back 174

Back (Definition)

Front 175

half angle stuff

Back 175

Back (Definition)

Front 176

half angle stuff

Back 176

Back (Definition)

Front 177

trig identity sec

Back 177

Back (Definition)

Front 178

integration by parts

Back 178

Back (Definition)

Front 179

trig sub sin

Back 179

Back (Definition)

Front 180

trig sub tan

Back 180

Back (Definition)

Front 181

mean value theorem

Back 181

Back (Definition)

Front 182

average value

Back 182

Back (Definition)

Front 183

D (sec^ -1 x)

Back 183

Back (Definition)

Front 184

D(tan^-1 x)

Back 184

Back (Definition)

Front 185

relationship between cot and csc

Back 185

Back (Definition)

Front 186

sin2ø

Back 186

Back (Definition)

Front 187

half angle stuff

Back 187

Back (Definition)

Front 188

half angle stuff

Back 188

Back (Definition)

Front 189

trig identity sec

Back 189

Back (Definition)

Front 190

integration by parts

Back 190

Back (Definition)

Front 191

trig sub sin

Back 191

Back (Definition)

Front 192

trig sub tan

Back 192

Back (Definition)

Front 193

mean value theorem

Back 193

Back (Definition)

Front 194

trig sub sin

Back 194

Back (Definition)

Front 195

trig sub tan

Back 195

Back (Definition)

Front 196

mean value theorem

Back 196

Back (Definition)

Front 197

average value

Back 197

Back (Definition)

Front 198

d of logs

Back 198

Back (Definition)