Nshs Ap Calculus

Front 1

lim f(x)
x->infinity

Back 1

Horizontal Asymptotes
BOBO BOTN EATS DC

Front 2

Derivative fails to exist

Back 2

Discontinuity
Vertical tangent line
Cusp, Sharp turn

Front 3

Definition of continuity

Back 3

Front 4

sin 2x

Back 4

2 sinx cosx

Front 5

cos 2x

Back 5

cos^2 x - sin^2 x

Front 6

ln e

Back 6

1

Front 7

ln 1

Back 7

0

Front 8

Horizontal Asymptotes

Back 8

lim f(x)
x->infinity

BOBO BOTN EATS DC

Front 9

Quotient identity for tan x

Back 9

sin x
------
cos x

Front 10

Quotient identity for cot x

Back 10

cos x
-------
sin x

Front 11

Reciprocal identity for csc x

Back 11

1
-----
sin x

Front 12

Reciprocal identity for sec x

Back 12

1
-----
cos x

Front 13

Pythagorean identity with sin x

Back 13

sin^2 x + cos^2 x = 1

Front 14

Pythagorean identity with tan x

Back 14

1 + tan^2 x = sec^2 x

Front 15

Pythagorean identity with cot x

Back 15

1 + cot^2 x = csc^2 x

Front 16

(a + b)^2

Back 16

a^2 + 2ab + b^2

Front 17

a^2 - b^2

Back 17

(a + b)(a - b)

Front 18

f'(x) > 0

Back 18

f(x) is increasing

Front 19

f'(x) < 0

Back 19

f(x) is decreasing

Front 20

f'(x) = 0 or undefined
changes positive to negative

Back 20

Relative maximum

Front 21

f(x) is increasing

Back 21

f'(x) > 0

Front 22

f(x) is decreasing

Back 22

f'(x) < 0

Front 23

Relative maximum

Back 23

f'(x) = 0 or undefined
changes positive to negative

Front 24

f'(x) = 0 or undefined
changes negative to positive

Back 24

Relative minimum

Front 25

Relative minimum

Back 25

f'(x) = 0 or undefined
changes negative to positive

Front 26

Limit Definition of the Derivative

Back 26

Front 27

Area of a Trapzoid

Back 27

Front 28

f(x) is concave up

Back 28

f"(x) > 0

f'(x) is increasing

Front 29

f(x) is concave down

Back 29

f"(x) < 0

f'(x) is decreasing

Front 30

f"(x) > 0

Back 30

f(x) is concave up

f'(x) is increasing

Front 31

f"(x) < 0

Back 31

f(x) is concave down

f'(x) is decreasing

Front 32

inflection point

Back 32

f"(x) = 0 or undefined AND changes signs

f'(x) changes from incr to decr or decr to incr

Front 33

Derivative of k

Back 33

0 (zero)

Front 34

Derivative of x^n

Back 34

n*x^(n-1)

Front 35

Derivative of f*g

Back 35

f*g' + g*f'

Front 36

Derivative of f/g

Back 36

(g*f' - f*g')/g^2

Front 37

Derivative of Ln x

Back 37

1/x

Front 38

Derivative of e^x

Back 38

e^x

Front 39

Derivative of a^x

Back 39

(a^x)(ln a)

Front 40

Derivative of f(g(x))

Back 40

f'(g(x))*g'(x)

Front 41

Derivative of sin x

Back 41

cos x

Front 42

Derivative of cos x

Back 42

- sin x

Front 43

Derivative of tan x

Back 43

sec^2 x

Front 44

Derivative of cot x

Back 44

-csc^2 x

Front 45

Derivative of sec x

Back 45

sec x tan x

Front 46

Derivative of csc x

Back 46

-csc x cot x

Front 47

Equation of a Tangent Line

Back 47

y = f(a) + f'(a)(x - a)

Front 48

Average Rate of Change

Back 48

[f(b)-f(a)]/(b-a)

Front 49

Average value

Back 49

1/(b-a) * Integral[f(x) dx]

Front 50

Total Distance Traveled

Back 50

Integral (abs val[v(t)]) dt

Front 51

Displacement

Back 51

Integral [v(t)] dt

Front 52

Position

Back 52

Integral of velocity

Front 53

Velocity

Back 53

Derivative of position
Integral of acceleration

Front 54

Acceleration

Back 54

Derivative of Velocity
Second Derivative of Position

Front 55

Back 55

Horizontal Asymptotes
BOBO BOTN EATSDC

Front 56

Displacement

Back 56

Front 57

Total Distance Traveled

Back 57

Front 58

Average Value

Back 58

Front 59

Average Rate of Change

Back 59