Stuff to memorize for the AP Calculus Test

studied byStudied by 162 people
4.5(6)
Get a hint
Hint

Y=f(x) must be continuous at each:

1 / 63

64 Terms

1

Y=f(x) must be continuous at each:

-Critical Point or undefined and endpoints

New cards
2

Local Minimum

Goes (-,0,+) or (-, und, +)

New cards
3

Local Maximum

Goes (+,0,-) or (+, und, -)

New cards
4

Point of Inflection

  • Concavity Changes

  • (+,0,-) or (-,0,+)

  • (+,und,-) or (-,und,+)

New cards
5

D/dx(sinx)

Cosx

New cards
6

D/dx(cosx)

-sinx

New cards
7

D/dx(tanx)

Sec²x

New cards
8

D/dx(cotx)

-csc²x

New cards
9

D/dx(secx)

Secxtanx

New cards
10

D/dx(cscx)

-cscxcotx

New cards
11

D/dx(lnx)

1/x

New cards
12

D/dx(ln(n))

1/n

New cards
13

D/dx(eⁿ)

Eⁿ

New cards
14

∫Cosx

Sinx

New cards
15

∫-sinx

Cosx

New cards
16

∫Sec²x

Tanx

New cards
17

∫-csc²x

Cotx

New cards
18

∫Secxtanx

Secx

New cards
19

∫-cscxcotx

Cscx

New cards
20

∫1/n

Ln(n)

New cards
21

∫Eⁿ

Eⁿ

New cards
22

When doing integrals never forget

Constant (+c)

New cards
23

∫Axⁿ

A/n+1(xⁿ⁺¹)+C

New cards
24

∫Tanx

  • Ln|secx|+c

  • Ln|cosx|+c

New cards
25

∫Secx

Ln|secx+tanx|+c

New cards
26

D/dx(sin⁻¹u)

1/√1-u²

New cards
27

D/dx(cos⁻¹x)

-1/√1-x²

New cards
28

D/dx(tan⁻¹x)

1/1+x²

New cards
29

D/dx(cot⁻¹x)

-1/1+x²

New cards
30

With derivative inverses

You plug in the number of the trigonometric function into x

New cards
31

D/dx(sec⁻¹x)

1/|x|√x²-1

New cards
32

D/dx(csc⁻¹x)

-1/|x|√x²-1

New cards
33

D/dx(aⁿ)

Aⁿln(a)

New cards
34

D/dx(Logₙx)

1/xln(a)

New cards
35

Chain Rule

  • Take derivative of outside of parenthesis

  • Take derivative of inside parenthesis and keep the original of what was in the parenthesis

  • For example, sin(x²+1)→ 2xcos(x²+1)

New cards
36

Product Rule

d/dx first times second + first times d/dx second

New cards
37

Quotient Rule

LoDHi-HiDLo/LoLo

New cards
38

Fundamental Theorem of Calculus

  • ∫(a to b) f(x) dx = F(b) - F(a)

  • Basically saying that F’(x)=f(x)

New cards
39

f relative max→f ‘ goes from

Positive to negative

New cards
40

f relative min→f ‘ goes from

Negative to positive

New cards
41

Intermediate Value Theorem

If I pick an X value that is included on a continuous function, I will get a Y value, within a certain range, to go with it.

New cards
42

Mean Value Theorem

If function is continuous on [a,b] and first derivative exist on interval (a,b), then there is at least one number (c) such that f’(c)=f(b)-f(a)/b-a

New cards
43

Rolle’s Theorem with Mean Value Theorem

If function is continuous on [a,b] and first derivative exist on interval (a,b), and f(a)=f(b) then there is at least one number x=c such that f’(c)=0

New cards
44

Trapezoidal Rule

The average of left hand point method and right hand point method

New cards
45

Theorem of mean value and average value

1/b-a ∫f(x)dx which is the average value

New cards
46

Disk Method

V=π∫[R(x)]²dx

New cards
47

Washer Method

π∫(R(x))²-(r(x))²dx

New cards
48

General volume equation

V=∫area(x)dx

-If no shape is given, then you just take the integral of the function

New cards
49

Distance, Velocity, and Acceleration

Velocity is d/dx of position

Acceleration is d/dx of velocity

New cards
50

Displacement

∫(Velocity)dt

New cards
51

Distance

∫|Velocity|dt

New cards
52
New cards
53

Speed

The absolute value of velocity

New cards
54

Average Velocity

Final Position-Initial Position/Total time

New cards
55

cos(0)

1

New cards
56

sin(0)

0

New cards
57

Pie circle starts with

π/6

New cards
58

tan(π/3)

√3

New cards
59

tan(π/6)

√3/3

New cards
60

tan(90⁰)

Undefined

New cards
61

Double Argument

sin2x=2sinxcosx

cos2x=cos²x-sin²x=1-2sin²x

cos²x=1/2(1+cos2x)

sin²x=1/2(1-cos2x)

New cards
62

Pythagorean Identity

sin²x+cos²x=1

New cards
63
New cards
64

L’Hopital Rule

If limit equals 0/0 or ∞/∞, then you can take the derivative

New cards

Explore top notes

note Note
studied byStudied by 78 people
Updated ... ago
5.0 Stars(6)
note Note
studied byStudied by 14 people
Updated ... ago
5.0 Stars(1)
note Note
studied byStudied by 250 people
Updated ... ago
5.0 Stars(1)
note Note
studied byStudied by 4 people
Updated ... ago
5.0 Stars(1)
note Note
studied byStudied by 21 people
Updated ... ago
4.0 Stars(1)
note Note
studied byStudied by 43 people
Updated ... ago
5.0 Stars(2)
note Note
studied byStudied by 12 people
Updated ... ago
5.0 Stars(1)
note Note
studied byStudied by 6 people
Updated ... ago
5.0 Stars(1)

Explore top flashcards

flashcards Flashcard52 terms
studied byStudied by 2 people
Updated ... ago
5.0 Stars(1)
flashcards Flashcard56 terms
studied byStudied by 10 people
Updated ... ago
5.0 Stars(1)
flashcards Flashcard161 terms
studied byStudied by 22 people
Updated ... ago
4.0 Stars(1)
flashcards Flashcard26 terms
studied byStudied by 2 people
Updated ... ago
5.0 Stars(1)
flashcards Flashcard29 terms
studied byStudied by 14 people
Updated ... ago
5.0 Stars(1)
flashcards Flashcard50 terms
studied byStudied by 15 people
Updated ... ago
5.0 Stars(2)
flashcards Flashcard49 terms
studied byStudied by 22 people
Updated ... ago
5.0 Stars(2)
flashcards Flashcard128 terms
studied byStudied by 7 people
Updated ... ago
5.0 Stars(1)