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logarithmic form

a=b^c in logarithmic form

logarithmic function

what is the common logarithm

an alternate way to write an exponential function

c=logba

function with general equation y=logbx b>0 and b CANNOT = 1 w…

logx implies log10x

logarithmic form

an alternate way to write an exponential function

a=b^c in logarithmic form

c=logba

Henry IV

Henry VIII

Anne Boleyn

Charles V, Holy Roman Empire

Sanctioned religious toleration of the Huguenots, French Calv…

A king of England in the early sixteenth century. With the su…

Queen of England from 1533 to 1536 as the second wife of King…

Was ruler of both the Spanish Empire from 1516 and the Holy R…

Henry IV

Sanctioned religious toleration of the Huguenots, French Calv…

Henry VIII

A king of England in the early sixteenth century. With the su…

exponential function

if b^x = b^y then...

compound interest formula

compounding continuously formula

function with a numeric (constant) base taken to a VARIABLE p…

x=y

A(t) is the amount after time t... P is the amount invested... r is…

A(t) is the amount after time t... P is the amount invested... r is…

exponential function

function with a numeric (constant) base taken to a VARIABLE p…

if b^x = b^y then...

x=y

absolute monarch

alliance

armada

autocratic

A ruler with complete authority over the government and the l…

formal agreement between two or more nations or powers to coo…

huge fleet of ships, such as the Spanish Armada that unsucces…

ruling with unlimited authority

absolute monarch

A ruler with complete authority over the government and the l…

alliance

formal agreement between two or more nations or powers to coo…

one to one function (1-1)

strictly monotonic

are all even degree polynomials monoto…

if there are no horizontal tangents, i…

a function whose inverse is also a function (the horizontal l…

1-1 functions that increase over its entire domain or decreas…

no

yes

one to one function (1-1)

a function whose inverse is also a function (the horizontal l…

strictly monotonic

1-1 functions that increase over its entire domain or decreas…

Slope

Terminal Velocity

Symmetric Difference

Logistic Growth Equation

average velocity/average rate of change/how fast you're going

When a falling object begins speeding up

Using either side of a point to find it's slope

p' = kP(1 - P/M)... k = natural exponential growth rate if nothi…

Slope

average velocity/average rate of change/how fast you're going

Terminal Velocity

When a falling object begins speeding up

Symbolic, generative, structured

Phoneme

Morpheme

Semantics

Imagine that a race of aliens comes to earth. These aliens qu…

The smallest unit of sound in a language is a _____

The smallest unit of meaning in a language is a ______

______ is the component of language concerned with understand…

Symbolic, generative, structured

Imagine that a race of aliens comes to earth. These aliens qu…

Phoneme

The smallest unit of sound in a language is a _____

Jaime Escalante was a teacher that hel…

Who played Anita in West Side Story an…

What city has the highest population o…

Who is famous for singing the song "La…

Calculus

Rita Moreno

New York City

Ritchie Valens

Jaime Escalante was a teacher that hel…

Calculus

Who played Anita in West Side Story an…

Rita Moreno

Events leading to the scientific revol…

scholasticism

Copernicus

Brahe

1. Discovery of the New World 2. Invention of the Printing Pr…

A philosophical and theological system, associated with Thoma…

Developed the first modern theory of a sun-centered universe…

Amassed nearly 20 years worth of astrological data that event…

Events leading to the scientific revol…

1. Discovery of the New World 2. Invention of the Printing Pr…

scholasticism

A philosophical and theological system, associated with Thoma…

Definition of a derivative

Definition of continuity

Average rate of change of f(x) on [a, b]

Rolle's theorem

lim as h->0 f(x+h) - f(x)/h

at c if ... 1. f(c) is defined ... 2. lim as x->c exists ... 3. lim as…

f(b) - f(a)/b-a

If f is continuous on [a,b] and differentiable on (a, b) and…

Definition of a derivative

lim as h->0 f(x+h) - f(x)/h

Definition of continuity

at c if ... 1. f(c) is defined ... 2. lim as x->c exists ... 3. lim as…

Average rate of change of f(x) on [a,b]

Rolle's Theorem

Mean Value Theorem

Intermediate Value Theorem

f'(c) = (f(b) - f(a)) / (b-a)

If f is continuous on [a,b] and differentiable on (a,b) and f…

If f is continuous on [a,b] and differentiable on (a,b), then…

If f is continuous on [a,b] and k is any number between f(a)…

Average rate of change of f(x) on [a,b]

f'(c) = (f(b) - f(a)) / (b-a)

Rolle's Theorem

If f is continuous on [a,b] and differentiable on (a,b) and f…

Extreme Value Theorem

Critical number

Rolle's Theorem

Mean Value Theorem

If f is continuous on a closed interval [a, b], then f has bo…

x-values of a function where f' = 0 or f' is not defined. Rel…

If f is continuous on a closed interval [a, b] and differenti…

If f is continuous on a closed interval [a, b] and differenti…

Extreme Value Theorem

If f is continuous on a closed interval [a, b], then f has bo…

Critical number

x-values of a function where f' = 0 or f' is not defined. Rel…

First Derivative Test

Definition of Concavity

Concavity Test

Second Derivative Test for Local Extrema

Use to find extrema ... (1) Find first derivative ... (2) Set equal…

The graph of a differentiable function y = f(x) is ... a) concav…

The graph of a twice differentiable function y = f(x) is ... a)…

(1) If f'(c) = 0 and f''(c) < 0, then f has a local maximum a…

First Derivative Test

Use to find extrema ... (1) Find first derivative ... (2) Set equal…

Definition of Concavity

The graph of a differentiable function y = f(x) is ... a) concav…

**Ptolemy

Geocentric Model

Copernicus

On the Revolution of the Heavenly Sphe…

supported geocentric model, aka Ptolematic Model

the theory that the Earth was the stationary center of the un…

heliocentric model... On the Revolution of the Heavenly Spheres

Copernicus... proposed heliocentric model... published on his death…

**Ptolemy

supported geocentric model, aka Ptolematic Model

Geocentric Model

the theory that the Earth was the stationary center of the un…

Trapezoid Riemann Sum

Fundamental Theorem of Calculus 1 (FTC…

Fundamental Theorem of Calculus 2 (FTC…

Fundamental Theorem of Calculus 2 (FTC…

Tn = ∆x[.5f(x1) + f(x2) + ... + f(xn-1) + .5f(xn)]... (Average o…

See part one and use chain rule

Trapezoid Riemann Sum

Tn = ∆x[.5f(x1) + f(x2) + ... + f(xn-1) + .5f(xn)]... (Average o…

Fundamental Theorem of Calculus 1 (FTC…

lim x→±∞ (f(x)/g(x)) = 0 if....

lim x→±∞ (f(x)/g(x)) = ∞ if...

lim x→±∞ (f(x)/g(x)) = ratio of coeffi…

Mean Value Theorem

degree of g(x) > degree of f(x)

degree of f(x) > degree of g(x)

degree of f(x) = degree of g(x)

If f is continuous on [a,b] and differentiable on (a,b), then…

lim x→±∞ (f(x)/g(x)) = 0 if....

degree of g(x) > degree of f(x)

lim x→±∞ (f(x)/g(x)) = ∞ if...

degree of f(x) > degree of g(x)

right triangles with natural number le…

(f * g)(x) =

if -x for x results in an equivalent e…

if -y for y results in an equivalent e…

3-4-5, 5-12-13, 8-15-17, 7-24-25

f(g(x))

is symmetric about the y axis

is symmetric about the x axis

right triangles with natural number le…

3-4-5, 5-12-13, 8-15-17, 7-24-25

(f * g)(x) =

f(g(x))

Sum/Difference of limits ... [lim f(x) ±…

Scalar multiplication ... [lim a*f(x)]

Product of limits... [lim f(x) * lim g(x)]

Quotient of limits... [lim f(x) ÷ lim g(x…

limit of the sums/difference ... [lim (f(x) ± g(x))]

a*lim f(x)

limit of products... lim [f(x) * g(x)]

Limit of quotients... lim [f(x) ÷ g(x)]

Sum/Difference of limits ... [lim f(x) ±…

limit of the sums/difference ... [lim (f(x) ± g(x))]

Scalar multiplication ... [lim a*f(x)]

a*lim f(x)

definition of derivative

three places where functions are not d…

if f is differentiable at x=c,

Implicit differentiation

f'(x) = lim as h->0 of [f(x+h) - f(x)]/h

1. discontinuities... 2. sharp turn... 3. vertical tangent

then f is continuous at x=c

used when y cannot be written explicitly as a function of x

definition of derivative

f'(x) = lim as h->0 of [f(x+h) - f(x)]/h

three places where functions are not d…

1. discontinuities... 2. sharp turn... 3. vertical tangent

aristotle/ ptolemy

copernicus

kepler

galileo

held that the earth was center of the universe (Geocentric th…

stated that the earth rotated on its axis around the sun (hel…

used math to prove planets orbit around sun

improved telescope, established experimentation set forth law…

aristotle/ ptolemy

held that the earth was center of the universe (Geocentric th…

copernicus

stated that the earth rotated on its axis around the sun (hel…

Rolle's Theorem

Mean Value Theorem

Fundamental Theorem of Calculus

Second Fundamental Theorem of Calculus

Let f be continuous on [a,b] and differentiable on (a,b)... If…

If f is continuous on [a,b] and differentiable on (a,b), then…

Let f(x) be integrable (continuous) on [a,b] and let F(x) be…

Rolle's Theorem

Let f be continuous on [a,b] and differentiable on (a,b)... If…

Mean Value Theorem

If f is continuous on [a,b] and differentiable on (a,b), then…

education

hidden curriculum

schooling in capitalist america

schools

he process through which academic, social, and cultural ideas…

nonacademic and less over socialization functions of schoolin…

"the educational system...is best understood as an institutio…

help to reinforce and maintain inequalities found within the…

education

he process through which academic, social, and cultural ideas…

hidden curriculum

nonacademic and less over socialization functions of schoolin…

Extreme Value Theorem

Critical Number

Rolle's Theorem

Mean Value Theorem

If f is continuous on a closed interval [a,b], then f has bot…

x values of a function where f'=0 or f' is not defined. Relat…

If f is continuous on a closed interval [a,b] and differentia…

If f is continuous on a closed interval [a,b] and differentia…

Extreme Value Theorem

If f is continuous on a closed interval [a,b], then f has bot…

Critical Number

x values of a function where f'=0 or f' is not defined. Relat…

Find where f'(x)=0 or undefined, sign…

Find where f'(x)=0 or undefined, sign…

Find where f''(x)=0 or undefined, sign…

Find where f''(x)=0 or undefined, sign…

Increasing intervals

Decreasing intervals

Concave up

Concave down

Find where f'(x)=0 or undefined, sign…

Increasing intervals

Find where f'(x)=0 or undefined, sign…

Decreasing intervals

[k × u]' = where k is a real number, a…

[u ± v]' = where u and v are functions…

[u × v]' = where u and v are functions…

[u/v]' = where u and v are functions o…

k × u'

u' ± v'

(u)(v)' + (u)'(v)

(v)(u)' - (u)(v)' / (v)²

[k × u]' = where k is a real number, a…

k × u'

[u ± v]' = where u and v are functions…

u' ± v'

'God's Handiwork"

"natural philosophers"

Alchemy and hermetic magic

Ptolemaic Universe

The world around them. Many educated Europeans were intereste…

medieval scientists that preferred refined logical analysis t…

Tradition believed that the world was a living embodiment of…

Universe seen as a series of concentric spheres with a fixed…

'God's Handiwork"

The world around them. Many educated Europeans were intereste…

"natural philosophers"

medieval scientists that preferred refined logical analysis t…

Intermediate Value Theorem

Average Rate of Change

Instantenous Rate of Change

Formal definition of derivative

If f(1)=-4 and f(6)=9, then there must be a x-value between 1…

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(1)=-4 and f(6)=9, then there must be a x-value between 1…

Average Rate of Change

Slope of secant line between two points, use to estimate inst…

Extreme Value Theorum

Rolle's Theorum

Mean Value Theorum

Critical Number

If f is continuous on a closed interval [a,b], then f has an…

Let f be continuous on the closed interval [a,b] and differen…

If f is continuous on the closed [a,b] and differentiable on…

Let f be defined at c. If f'(c)=0 or if f'(x) is not defined…

Extreme Value Theorum

If f is continuous on a closed interval [a,b], then f has an…

Rolle's Theorum

Let f be continuous on the closed interval [a,b] and differen…

Area between Curves (up and down)

Area between Curves (side to side)

Area between Curves (weave)

Volume

∫ upper - lower... integrate over "x"... - use "x" values as limit…

∫ right - left... integrate over "y"... - use "y" values as limits…

∫ | f(x) - g(x) |... integrate over "x" or "y", depending on ca…

V = ∫ Area of Cross Section

Area between Curves (up and down)

∫ upper - lower... integrate over "x"... - use "x" values as limit…

Area between Curves (side to side)

∫ right - left... integrate over "y"... - use "y" values as limits…

Copernicus

Kepler

Galileo

Newton

-started an idea of heliocentrism... -believed that earth's orbi…

-Three laws of planetary motion, on elliptical orbit, and two…

-Developed a new telescope... -Observed the moon and it's crater…

-(1643-1727)... -invented Calculus... -originated the theory of gra…

Copernicus

-started an idea of heliocentrism... -believed that earth's orbi…

Kepler

-Three laws of planetary motion, on elliptical orbit, and two…

Thirty Years War

States that centralized in 17th century

States that didn't centralize in 17th…

Absolute Monarchs of the 17th century

Bourbon kings of France vs surrounding Spanish and Austrian H…

England, France, Austria, Prussia, and Russia.

United netherlands, ottoman empire, poland, Sweden

Louis XIV of France "the sun king", Hohenzollern rulers in Br…

Thirty Years War

Bourbon kings of France vs surrounding Spanish and Austrian H…

States that centralized in 17th century

England, France, Austria, Prussia, and Russia.