Study sets matching "ap calculus"

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Study sets matching "ap calculus"

69 termscreated on January 20, 2017
AP Calculus AB Exam
Intermediate Value Theorem
Average Rate of Change
Instantenous Rate of Change
Formal definition of derivative
if f(x) is continuous on [a, b], all y-values between f(a) an…
Slope of secant line between two points, use to estimate inst…
Slope of tangent line at a point, value of derivative at a po…
limit as h approaches 0 of [f(a+h)-f(a)]/h
Intermediate Value Theorem
if f(x) is continuous on [a, b], all y-values between f(a) an…
Average Rate of Change
Slope of secant line between two points, use to estimate inst…
12 termscreated on January 20, 2017
Picture Monolouge
Hello everybody, and welcome back to s…
No grumpy cats in my class!
Yes, we have to do the work (eye roll)…
Oh gee, it seems I have forgotten to i…
Now I know that everyone is probably a little melancholy abou…
This is going to be the most hip year ever!
What's that?
Hi, I'm Ms. Fisher, this is my first year here at Lake Pointe…
Hello everybody, and welcome back to s…
Now I know that everyone is probably a little melancholy abou…
No grumpy cats in my class!
This is going to be the most hip year ever!
6 termscreated on January 20, 2017
AP Calculus BC - Applications of Definite Integrals
Area between curves on a plane
Volume of a solid of revolution using…
Volume of a solid of revolution using…
Volume of a solid of revolution using…
∫ f(upper curve) dx - ∫ f(lower curve) dx, from a-b
π ∫ (f(x))² dx, from a-b
π ∫ (f(outer radius))² dx - π ∫ (f(inner radius))² dx, from a-b
2π ∫ (shell radius)(shell height) dy, from a-b
Area between curves on a plane
∫ f(upper curve) dx - ∫ f(lower curve) dx, from a-b
Volume of a solid of revolution using…
π ∫ (f(x))² dx, from a-b
28 termscreated on January 20, 2017
ApEuro Unit 4 - The Scientific Revolution
Contributors to Scientific Revolution
Geocentric
Heliocentric
Nicolaus Copernicus
- The Renaissance... - New technologies and methods... - The Reform…
Earth-centered view of universe
Sun-centered view of universe
Offered idea of a heliocentric model of the universe
Contributors to Scientific Revolution
- The Renaissance... - New technologies and methods... - The Reform…
Geocentric
Earth-centered view of universe
87 termscreated on January 20, 2017
AP Calculus AB Knowledge
What conditions must be to satisfied f…
If the appropriate conditions are sati…
Limit
Quotient rule?
f(x) is continuous in the interval [a, b] and differentiable…
There is at least one point c in the interval (a, b) at which…
A limit is the value that a function or sequence "approaches"…
(vu'-uv')/v^2
What conditions must be to satisfied f…
f(x) is continuous in the interval [a, b] and differentiable…
If the appropriate conditions are sati…
There is at least one point c in the interval (a, b) at which…
12 termscreated on January 19, 2017
AP Calculus Mid-Terms
theorem on limits
sandwich theorem
limit as theta approaches 0 [sinθ/θ]
the function y=f(x) is continuous at x…
if lim f(x) and lim g(x) are finite numbers, then:... -lim kf(x)…
if f(x) ≤ g(x) ≤ h(x) and as limit x approaches to c of f(x)…
1
-f(c) exists; (that is, c is in the domain of f)... - as limit o…
theorem on limits
if lim f(x) and lim g(x) are finite numbers, then:... -lim kf(x)…
sandwich theorem
if f(x) ≤ g(x) ≤ h(x) and as limit x approaches to c of f(x)…
11 termscreated on January 19, 2017
AP World History Unit 5
ptomely
copernicus
harvey
galileo
he said the universe is earth centered
he said the sun is the center of the universe
study of the heart and how blood circulates through the body
the sun is the center of the universe with his telescope
ptomely
he said the universe is earth centered
copernicus
he said the sun is the center of the universe
11 termscreated on January 19, 2017
AP Calculus BC Midterm Review
Definition of the derivative
Definition of the derivative
Definition of continuity
Average rate of change of f(x) on [a,b]
f'(x)= lim h--->0 (f(x+h)-f(x))/h
f'(a)= lim x--->a (f(x)-f(a))/(x-a)
f is ______________ at c if... 1. f(c) is defined... 2. lim x--->c…
= (f(b)-f(a))/(b-a)
Definition of the derivative
f'(x)= lim h--->0 (f(x+h)-f(x))/h
Definition of the derivative
f'(a)= lim x--->a (f(x)-f(a))/(x-a)
11 termscreated on January 19, 2017
Basic and Trigonometric Integration Rules
∫0dx
∫kdx
∫kf(x)dx
∫[f(x) ± g(x)]dx
c
kx + c
k∫f(x)dx
∫f(x)dx ± ∫g(x)dx
∫0dx
c
∫kdx
kx + c
16 termscreated on January 19, 2017
Enlightenment Quick Check
Revolutions
Common Message is
Bill of Rights
Philosphes
Changes people's outlook, often based on coalition
English, American, and French revolutions are all labeled "de…
No taxation without representation
Mainly aethiests, coming up with new ideas
Revolutions
Changes people's outlook, often based on coalition
Common Message is
English, American, and French revolutions are all labeled "de…
29 termscreated on January 19, 2017
Misc. Info to Know
linear density p @ x
growth rate
dy/dx = ...
rate of reaction
p = limit as change in x approaches 0 of change in m over cha…
limit as change in t approaches 0 of change in n over change…
lim as change in x approaches 0 of change in y over change in x
d[C]/dt = d[A]/dt = -d[B]/dt
linear density p @ x
p = limit as change in x approaches 0 of change in m over cha…
growth rate
limit as change in t approaches 0 of change in n over change…
27 termscreated on January 19, 2017
AP Calculus BC Integrals to Know, Love, & Cherish
∫uⁿdu
∫du/u
∫(e^u)du
∫(a^u)du
[uⁿ⁺¹/(n+1)] + C
ln |u| + C
e^u + C
(a^u)/lna +c
∫uⁿdu
[uⁿ⁺¹/(n+1)] + C
∫du/u
ln |u| + C
32 termscreated on January 19, 2017
vocab ap world - loewen
Tokugawa Shogunate
Maroons
"Silver Drain"
Abolition
Last feudal Japanese military government, controlled Japan an…
escaped slaves
the concept of how most of the silver in late 1500's to early…
the act of abolishing or the state of being abolished; the en…
Tokugawa Shogunate
Last feudal Japanese military government, controlled Japan an…
Maroons
escaped slaves
8 termscreated on January 19, 2017
The Things They Carried Section 12: The Man I Killed
How did O'Brien kill the man he descri…
Name 3 details that O'Brien used to de…
What does O'Brien imagine about the ma…
What does Azar compare the man to?
A grenade in My Khe
His upper lip and teeth were missing, his jaw was in his thro…
He was born in 1946 and his parents were farmers. He was not…
Cereal
How did O'Brien kill the man he descri…
A grenade in My Khe
Name 3 details that O'Brien used to de…
His upper lip and teeth were missing, his jaw was in his thro…
13 termscreated on January 19, 2017
IOBE - Aestheticism
aestheticism
Where did the roots of aestheticism re…
Who were the dominant figures of Aesth…
The influence of D.G. Rossetti
a late 19th century literary movement that rested on the cred…
poetry of John Keats, Theopile Gautier's preface to Mademoise…
its origins had a close kinship to the reverence for beauty o…
The Aesthetic vogue of the later seventies & the eighties [in…
aestheticism
a late 19th century literary movement that rested on the cred…
Where did the roots of aestheticism re…
poetry of John Keats, Theopile Gautier's preface to Mademoise…
38 termscreated on January 19, 2017
Enlightened Age/French Revolution
First Estate
Bourgeoisie
Divine Right
Aristocrats
Estate to which the clergy belonged
Term for the "middle class"
Absolute monarchs claimed to rule this
People belonging to the nobility or Second Estate
First Estate
Estate to which the clergy belonged
Bourgeoisie
Term for the "middle class"
28 termscreated on January 19, 2017
AP AB Calc Formulas
derivative of sinx
derivative of cosx
derivative of tanx
derivative of cotx
cosx
-sinx
sec^2x
-csc^2x
derivative of sinx
cosx
derivative of cosx
-sinx
37 termscreated on January 19, 2017
AP Calculus Flash Cards
f is continuous at x=c if...
Intermediate Value Theorem
Limit Definition of a Derivative
nx^(n-1)
If f is continuous on [a,b] and k is a number between f(a) an…
f is continuous at x=c if...
Intermediate Value Theorem
If f is continuous on [a,b] and k is a number between f(a) an…
67 termscreated on January 19, 2017
AP Calculus Flash Cards
f is continuous at x=c if...
Intermediate Value Theorem
Global Definition of a Derivative
nx^(n-1)
If f is continuous on [a,b] and k is a number between f(a) an…
f is continuous at x=c if...
Intermediate Value Theorem
If f is continuous on [a,b] and k is a number between f(a) an…
29 termscreated on January 19, 2017
AP Calculus Final Exam
domain of a function
limits
limit shortcut rules (approaching infi…
trig derivatives
-denominator can't = 0... -square root: x>= number under root... -x…
1. substitution... 2. factor, cancel, substitution ... -rewrite tri…
-higher power on top: lim= + or - infinity... -higher power on b…
sinx=cosx... cosx=-sinx... tanx=sec^2x... cotx=-csc^2x... secx=secxtanx... c…
domain of a function
-denominator can't = 0... -square root: x>= number under root... -x…
limits
1. substitution... 2. factor, cancel, substitution ... -rewrite tri…
76 termscreated on January 19, 2017
AP Calculus AB Midterm (Ch. 1- 4.5)
limit value is a
if f(x) is continuous at x=c then
to find limit of given #
Squeeze Theorem
y value
lim x→c f(x) = f(c)
plug in # ( if not possible rationalize)
if there are 3 functions around a point, c, there is a less t…
limit value is a
y value
if f(x) is continuous at x=c then
lim x→c f(x) = f(c)
20 termscreated on January 19, 2017
Second Fundamental Theorem of Calculus
F'(x) = x³ - 3x² - 3
F'(x) = -x³ + 4x² - 7
F'(x) = 5x¹÷³
F'(x) = 5√t
F'(x) = x³ - 3x² - 3
F'(x) = -x³ + 4x² - 7
11 termscreated on January 19, 2017
Basic Integration Rules
∫ 0 dx
∫ k dx
∫ k f(x) dx
∫ [f(x) ± g(x)] dx
C
kx + C
k ∫ f(x) dx
∫ f(x) dx ± ∫ g(x) dx
∫ 0 dx
C
∫ k dx
kx + C
27 termscreated on January 19, 2017
Trigonometry for AP Calculus AB
Derivative of sin(x)
Derivative of cos(x)
Derivative of tan(x)
Derivatice of csc(x)
Cos(x)
-sin(x)
sec^2(x)
-csc(x)cot(x)
Derivative of sin(x)
Cos(x)
Derivative of cos(x)
-sin(x)
26 termscreated on January 19, 2017
Midterm Derivatives and Antiderivatives
f(x) = x^a
f(x) = x^a
f(x) = x^-1
f(x) = x^-1
f'(x) = ax^(a-1)
F(x) = (x^(a+1))/(a + 1) + c
f'(x) = -x^-2
F(x) = ln|x| + c
f(x) = x^a
f'(x) = ax^(a-1)
f(x) = x^a
F(x) = (x^(a+1))/(a + 1) + c
29 termscreated on January 19, 2017
Midterm Definitions & Theorems
The Mean Value Theorem states that if…
Provided that the limit exists, the de…
A function is differentiable at x = a…
A function is continuous at x = c if a…
. . .there exists a c in (a, b), such that f'(c) = (f(b) - f(…
. . .f'(a) = lim(h->0) (f(a + h) - f(a)) / (h) or lim(x->a) (…
. . .f'(a) exists
. . .lim(x->c) f(x) = f(c)
The Mean Value Theorem states that if…
. . .there exists a c in (a, b), such that f'(c) = (f(b) - f(…
Provided that the limit exists, the de…
. . .f'(a) = lim(h->0) (f(a + h) - f(a)) / (h) or lim(x->a) (…
6 termscreated on January 18, 2017
Derivatives of Trig Functions
sinx
cosx
tanx
cotx
cosx
-sinx
sec^2x
-csc^2x
sinx
cosx
cosx
-sinx
13 termscreated on January 18, 2017
AP Calc AB Semester 1 Final
y = -f(x)
y = f(-x)
y = cf(x)
y = f(cx)
reflects across x-axis
reflects across y-axis
c > 1 : stretches vertically... 0 < c < 1 : shrinks vertically
c > 1 : shrinks horizontally... 0 < c < 1 : stretches horizontally
y = -f(x)
reflects across x-axis
y = f(-x)
reflects across y-axis
19 termscreated on January 18, 2017
AP Calculus
where f is increasing, f'
where f is decreasing, f'
where f has an extrema or a saddle poi…
where f is not continuous, has a cusp,…
> 0
< 0
= 0
is undefined
where f is increasing, f'
> 0
where f is decreasing, f'
< 0
30 termscreated on January 18, 2017
the Earth and its Peoples Chapter 16
scientific revolution
for sins, church gave
enlightenment
joint-stock
natural world works the ways it does
indulgences
using knowledge to see how humans react
modern time selling stock
scientific revolution
natural world works the ways it does
for sins, church gave
indulgences
23 termscreated on January 18, 2017
AP Calc BC Midterm: Do You Know Your Stuff?
derivative of sinx
derivative of cosx
derivative of tanx
derivative of cotx
cosx
-sinx
sec²x
-csc²x
derivative of sinx
cosx
derivative of cosx
-sinx
11 termscreated on January 18, 2017
derivatives+integrals
d/dx(ln(u))
d/dx(loga(f(x))
d/dx(e^u)
d/dx(a^u)
u'/u
f'(x)/f(x)ln(a)
e^u(u')
a^u(lna)(u')
d/dx(ln(u))
u'/u
d/dx(loga(f(x))
f'(x)/f(x)ln(a)
27 termscreated on January 18, 2017
AP World History Chapter 10 part 3 GREECE
Claudius Ptolemy was a
what is hellenistic
what cultures did hellenism consist of
Who did alexander kill
scientist
hybrid culture
mostly greek, egypt, and persia
his father
Claudius Ptolemy was a
scientist
what is hellenistic
hybrid culture
18 termscreated on January 18, 2017
AP Calculus AB Semester 1 Exam Review
y' sin x =
y' cos x =
y' tan x =
y' sec x =
cos x
-sin x
sec^2 x
sec (x) * tan (x)
y' sin x =
cos x
y' cos x =
-sin x
22 termscreated on January 18, 2017
Calculus 1/20
kn
[n(n+1)]/2
[n(n+1)(2n+1)]/6
[n²(n+1)²]/4
∑k
∑i
∑i²
∑i³
kn
∑k
[n(n+1)]/2
∑i
22 termscreated on January 18, 2017
AP Calculus Memorization
sin^2 (x) + cos^2 (x) =
1 + tan^2 (x) =
1 + cot^2 (x)
sin (x) =
= 1
= sec^2 (x)
csc^2 (x)
= 1 / csc(x)
sin^2 (x) + cos^2 (x) =
= 1
1 + tan^2 (x) =
= sec^2 (x)
20 termscreated on January 18, 2017
Calculus Theorems
Main Limit Theorem
Squeeze Theorem
Intermediate Value Theorem
Max-and-Min Theorem
- sum of limits equals limit of sum... - difference of limits eq…
If f(x) is continuous in a closed interval, then there is a v…
must be a maximum and minimum value of the function within a…
Main Limit Theorem
- sum of limits equals limit of sum... - difference of limits eq…
Squeeze Theorem
8 termscreated on January 18, 2017
Unit 4 Formulas
Mean Value Theorem for Integrals
Average Value Theorem
First Fundamental Theorem of Calculus
Second Fundamental Theorem of Calculus
Mean Value Theorem for Integrals
Average Value Theorem
6 termscreated on January 18, 2017
trig derivatives
f(x)=sinx
f(x)=cosx
f(x)=tanx
f(x)=cotx
f'(x)=cosx
f'(x)=-sinx
f'(x)=sec^2x
f'(x)=-csc^2x
f(x)=sinx
f'(x)=cosx
f(x)=cosx
f'(x)=-sinx
6 termscreated on January 18, 2017
Breakthroughs in medicine and chemistry
Who is Robert Boyle
Who is issac newton
What is calculus
What is gravity
Explained that all matter is composed of tiny particles that…
The father of calculus and gravity
Branch breakthof mathematics developed by issac newton
Single force that keeps the planets in their orbits around th…
Who is Robert Boyle
Explained that all matter is composed of tiny particles that…
Who is issac newton
The father of calculus and gravity
6 termscreated on January 18, 2017
Trigonometric derivatives and their inverses
d/dx (sin(x))
d/dx (sec(x))
d/dx (tan(x))
d/dx (cot(x))
cosine(x)
sec(x) * tan(x)
sec^2(x)
-cosecant(x) *-cot(x)
d/dx (sin(x))
cosine(x)
d/dx (sec(x))
sec(x) * tan(x)
15 termscreated on January 18, 2017
AP Calculus Formulas
What is the definition of e?
What is absolute value?
What is the definition of a derivative?
What is the definition of continuity?
e=lim(n→∞) (1+(1/n))ⁿ
x if x≥0... -x if x<0
lim(h→∞) (ƒ(x+h)-ƒ(x))/h
1) ƒ(c) is defined... 2) lim(x→c) ƒ(x) exists... 3) lim(x→c) ƒ(x)=ƒ…
What is the definition of e?
e=lim(n→∞) (1+(1/n))ⁿ
What is absolute value?
x if x≥0... -x if x<0
26 termscreated on January 18, 2017
expresate 3 chapter 3-1 los sustantivos
el álgebra
el cálculo
las ciencias sociales
el consejero
algebra
calculus
social studies
counselor
el álgebra
algebra
el cálculo
calculus
27 termscreated on January 18, 2017
AP Macroeconomics Unit 1
absolute advantage
allocative efficiency
black market
capital
the advantage conferred by the ability to produce more of a g…
an output level where the price equals the Marginal Cost (MC)…
a market in which goods or services are bought and sold illeg…
manufactured goods used to make other goods and services... For…
absolute advantage
the advantage conferred by the ability to produce more of a g…
allocative efficiency
an output level where the price equals the Marginal Cost (MC)…
27 termscreated on January 18, 2017
AP Salivary Glands
Type of Glands
Complex Glands
Compound Racemose Glands
Serous Secretion
Complex... Compound Racemose
Acini discharge into ducts
Have special epithelial secretory cells from Acini
Thin, watery... Polyhedral cells
Type of Glands
Complex... Compound Racemose
Complex Glands
Acini discharge into ducts
7 termscreated on January 17, 2017
MIDTERM STUFF
derivative sin-1
cos-1
tan-1
sec-1
1/squareroot 1-x^2
-1/square 1-x^2
1/1+x^2
1/|x| square x^2-1
derivative sin-1
1/squareroot 1-x^2
cos-1
-1/square 1-x^2
18 termscreated on January 17, 2017
AP Calculus BC Sem 2
L'Hopital's Rule
Indeterminate forms
Volume by disc
Volume by washer
1. 0/0... 2. ∞/∞... 3. 1^∞... 4. 0^0... 5. ∞±∞... 6. 0×∞
L'Hopital's Rule
Indeterminate forms
1. 0/0... 2. ∞/∞... 3. 1^∞... 4. 0^0... 5. ∞±∞... 6. 0×∞
17 termscreated on January 17, 2017
Series and Sequences
sequence
Series
recursive formula
explicit formula
set of real numbers separated by commas (,)
set of real numbers separated by addition signs (+)
shows how to find the next term using the previous term, a1 i…
A formula that allows direct computation of any (nth) term fo…
sequence
set of real numbers separated by commas (,)
Series
set of real numbers separated by addition signs (+)
22 termscreated on January 17, 2017
AP Calculus AB - Chapter 5
ln(ab)
ln(a/b)
lna^n
d/dx[lnx]
lna + lnb
lna - lnb
nlna
1/x
ln(ab)
lna + lnb
ln(a/b)
lna - lnb
21 termscreated on January 17, 2017
AP Calculus - Derivatives of Functions
d/dx c
d/dx e^x
d/dx b^x
d/dx sin(x)
0
e^x
b^x log(b) or.... b^x lnb
cos(x)
d/dx c
0
d/dx e^x
e^x
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