BC Definitions and Some AB

studied byStudied by 30 people
0.0(0)
learn
LearnA personalized and smart learning plan
exam
Practice TestTake a test on your terms and definitions
spaced repetition
Spaced RepetitionScientifically backed study method
heart puzzle
Matching GameHow quick can you match all your cards?
flashcards
FlashcardsStudy terms and definitions

1 / 56

flashcard set

Earn XP

Description and Tags

bc and ab basic shit

57 Terms

1

Integration By Parts

∫udv = uv -∫ [vdu]

<p>∫udv = uv -∫ [vdu]</p>
New cards
2

Geometric Series

infinite series of ar^n
a= first term, r =common ratio
from n=0 to infinity of ∑ ar^n

<p><span>infinite series of </span>ar^n<br>a= first term, r =common ratio<br>from n=0 to infinity of ∑ ar^n</p><p></p>
New cards
3

Taylor Series Formula

<p></p>
New cards
4

Maclaurin Series Formula

  • Maclaurin series is a Taylor series but not vice versa

<ul><li><p>Maclaurin series is a Taylor series but not vice versa</p></li></ul>
New cards
5

sin(x) Maclaurin Series

knowt flashcard image
New cards
6

cos(x) Maclaurin Series

knowt flashcard image
New cards
7

1(1+x) Maclaurin Series

knowt flashcard image
New cards
8

arctan(x) Maclaurin Series

knowt flashcard image
New cards
9

1/(1-x) Maclaurin Series

<p></p>
New cards
10

ln(1+x) Maclaurin Series

knowt flashcard image
New cards
11

e^x Maclaurin Series

knowt flashcard image
New cards
12

Lagrange Error Bound

<p></p>
New cards
13

Alternating Series Error Bound

knowt flashcard image
New cards
14

Divergence/nth term test

<p></p>
New cards
15

Ratio Test

knowt flashcard image
New cards
16

nth Root Test

<p></p>
New cards
17

Integral Test

knowt flashcard image
New cards
18

Alternating Series Test

knowt flashcard image
New cards
19

P-series Test

knowt flashcard image
New cards
20

Direct Comparison Test

knowt flashcard image
New cards
21

Limit Comparison Test

knowt flashcard image
New cards
22

Absolute Convergence Test

knowt flashcard image
New cards
23

Power Series General Form

knowt flashcard image
New cards
24

In Polar Cords what is x and y equal to?

tanθ = ?

x = rcos(θ) y= rsin(θ)

tan(θ) = y/x

Also

  • r² = x²+y²

  • θ = tan-1(y/x)

New cards
25

Area for Polar Curve

A = ½ ∫r²dθ

<p>A = ½ <span>∫r²d</span>θ</p>
New cards
26

slope for a polar curve

dy/dx = (dy/dθ)/(dx/dθ)

New cards
27

Slope for a parametric curve

dy/dx = (dy/dt)/(dx/dt)

New cards
28

Second derivative of a parametric curve

knowt flashcard image
New cards
29

Position, Velocity and Acceleration Vectors.

  • P = <x(t), y(t)>

  • V =<x’(t), y’(t)>

  • A = <x’’(t), y’’(t)>

New cards
30

Arc Length Formula

Remember Arc length parametric terms is simply distance formula

<p>Remember Arc length parametric terms is simply distance formula</p>
New cards
31

Speed Formula

<p></p>
New cards
32

Distance Formula

<p></p>
New cards
33

When is the Particle moving to the left and moving to the right?

Velocity = (-) , left

Velocity =(+), right

New cards
34

When is the particle speeding up/moving away from origin?

When Velocity and Acceleration are the same sign

New cards
35

Logistic Differential Equation General Form

dp/dt = kP(1 - P/C)

  • P = population at time t

  • C = carrying capacity

  • k = constant

<p>dp/dt = kP(1 - P/C)</p><ul><li><p>P = population at time t </p></li><li><p>C = carrying capacity </p></li><li><p>k = constant</p></li></ul>
New cards
36

Logistic Solution Form

P = c/(1+Ae^-kt)

New cards
37

Limacons Variations and General Equation

r = a±bcosθ or r = a±bsinθ

  • Inner Loop

  • Cardioid

  • Dimpled

  • Convex

<p>r = a±bcosθ or r = a±bsinθ</p><ul><li><p>Inner Loop</p></li><li><p>Cardioid</p></li><li><p>Dimpled</p></li><li><p>Convex</p></li></ul>
New cards
38

Rose Curves and General Equation

acos(nθ) or asin(nθ)

  • If n is odd, there are n petals

  • If n is even, there are 2n petals

First petal positions:

  • Cos curve - On the x-axis

  • Sin curve - First Quadrant

<p>acos(nθ) or asin(nθ)</p><ul><li><p>If n is odd, there are n petals</p></li><li><p>If n is even, there are 2n petals</p></li></ul><p>First petal positions:</p><ul><li><p>Cos curve -  On the x-axis</p></li><li><p>Sin curve - First Quadrant</p></li></ul>
New cards
39

Limacon Inner Loop Points

knowt flashcard image
New cards
40

Leminiscate General Equation

r = a²sinθ or a²cosθ

<p>r = a²sinθ or a²cosθ</p>
New cards
41

Circle General Equation

r = acosθ or asinθ

<p>r = acosθ or asinθ </p>
New cards
42

Spiral General Equation

r = θ

<p>r = θ</p>
New cards
43

Infinite Sum

knowt flashcard image
New cards
44

Finite sum

knowt flashcard image
New cards
45

Telescoping Series

First and last term are the only remaining terms within series.

<p>First and last term are the only remaining terms within series.</p>
New cards
46

Euler’s Method

knowt flashcard image
New cards
47

Inflection Point/POI

f’’(x) =0 or und and changes sign

New cards
48

Critical Point

f’(x) = 0 or und

New cards
49

Relative Min/Max

Min: f’ changes from (+) to (-) and f’ = 0 or und

f’ changes from (-) to (+) and f’ = 0 or und

New cards
50

What does concave up/down mean?

f’’ > 0 for concave up, f’’<0 for concave down

New cards
51

Tangent Line Eq/ Normal Line eq

Tangent Line: y-y1=m(x-x1)

Norm Line: y-y1=1/m(x-x1)

New cards
52

Riemann Sums

Right hand - overestimate for increasing functions and under for decreasing functions

Vice versa for Left hand

The Trapezoidal sum is the same as the average of the left and right Riemann sums (Goldilocks for estimating)

<p>Right hand - overestimate for increasing functions and under for decreasing functions</p><p>Vice versa for Left hand<br><br>The Trapezoidal sum is the same as the average of the left and right Riemann sums (Goldilocks for estimating)</p>
New cards
53

MVT

continuous on [a,b], and differentiable on open,

then exists x=c where f’(c ) =f(b)-f(a)/(b-a)

New cards
54

EVT

If F(x) is continuous on [a,b], then f has both an abs minimum and an abs max

New cards
55

IVT

If f(x) is continuous on [a,b], and k is between f(a) and f(b), and a<C<b then F(C) = k

New cards
56

Cross Section Volume Identities

<p></p>
New cards
57

Avg Value

<p></p>
New cards

Explore top notes

note Note
studied byStudied by 20 people
894 days ago
5.0(2)
note Note
studied byStudied by 1 person
50 days ago
5.0(1)
note Note
studied byStudied by 8 people
194 days ago
5.0(1)
note Note
studied byStudied by 5562 people
707 days ago
5.0(28)
note Note
studied byStudied by 21 people
904 days ago
5.0(3)
note Note
studied byStudied by 4 people
25 days ago
5.0(1)
note Note
studied byStudied by 12 people
738 days ago
5.0(1)
note Note
studied byStudied by 88 people
703 days ago
5.0(2)

Explore top flashcards

flashcards Flashcard (49)
studied byStudied by 21 people
370 days ago
5.0(1)
flashcards Flashcard (35)
studied byStudied by 840 people
291 days ago
5.0(1)
flashcards Flashcard (48)
studied byStudied by 1 person
61 days ago
5.0(1)
flashcards Flashcard (20)
studied byStudied by 10 people
710 days ago
5.0(1)
flashcards Flashcard (72)
studied byStudied by 3 people
667 days ago
5.0(1)
flashcards Flashcard (26)
studied byStudied by 58 people
357 days ago
5.0(1)
flashcards Flashcard (38)
studied byStudied by 3 people
226 days ago
5.0(1)
flashcards Flashcard (50)
studied byStudied by 86 people
675 days ago
5.0(2)
robot