# Study sets matching "ap calculus"

Nicolaus Copernicus

Johannes Kepler

Galileo Galilei

Francis Bacon

-The Earth rotated on its axis once daily... -Traveled around the…

-Planets move in oval paths called ellipses- not circles as Co…

-He built his own telescope. His discovery of moons circling p…

Claimed that ideas based solely on tradition or unproven facts…

Nicolaus Copernicus

-The Earth rotated on its axis once daily... -Traveled around the…

Johannes Kepler

-Planets move in oval paths called ellipses- not circles as Co…

Extreme Value Theorem

critical point

Fundamental Theorem of Calculus, Part I

Fundamental Theorem of Calculus, Part 2

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

a point in the interior of the domain of a function f at which…

Extreme Value Theorem

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

critical point

a point in the interior of the domain of a function f at which…

Vertical asymptotes

Intermediate Value Theorem

lim x-2 2-x/x^2-4

lim x-2 {x-2}/x-2

h(x)=f(x)/g(x) has a vertical asymptote at x=c

If f is continuous on the closed interval a b and k is any num…

-4

1

Vertical asymptotes

h(x)=f(x)/g(x) has a vertical asymptote at x=c

Intermediate Value Theorem

If f is continuous on the closed interval a b and k is any num…

Arc length

Partial Fractions Tips

Ssecxdx

Scscxdx

Sqrt{(dy)^2+(dx)^2}

If there is a degree difference of more than 1 between the num…

ln|secx+tanx|+c

-ln|cscx+cotx|+c

Arc length

Sqrt{(dy)^2+(dx)^2}

Partial Fractions Tips

If there is a degree difference of more than 1 between the num…

why is it important in calculus to stud…

max and min

extreme value theorum

increasing or decreasing

to the understanding of the characteristics of the graph of a…

• peaks and valleys... • usually occur when the derivative = 0 (…

if a function is continuous on a closed interval [a, b], then…

• increasing when the derivative is positive or above the x-ax…

why is it important in calculus to stud…

to the understanding of the characteristics of the graph of a…

max and min

• peaks and valleys... • usually occur when the derivative = 0 (…

Rolle's Theorem

Mean Value Theorem

Derivative gives...

First Derivative Test

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

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

Instantaneous rate of change

zeroes of first derivative give relative maxes/mins of functio…

Rolle's Theorem

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

Mean Value Theorem

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

Ferdinand involved Germany in Italian a…

The Hapsberg family, in the 16th centur…

German affairs became chaotic during th…

Which side did Louis XIII's Cardinal Ri…

Hapsbergs

Austria; Bohemia; Hungary; Spain; Naples; Milan; Sicily; Ameri…

Augsberg

Bohemian nobles

Ferdinand involved Germany in Italian a…

Hapsbergs

The Hapsberg family, in the 16th centur…

Austria; Bohemia; Hungary; Spain; Naples; Milan; Sicily; Ameri…

Charles I

Charles II

Christopher Columbus

Elizabeth I

English King during the English Civil War. his supporters were…

His becoming of kind of England was known as the Restoration s…

Born in Italy but sailed for Spain. He sailed to the Americas…

Ruled England after the death of Henry VIII. Defeated the Span…

Charles I

English King during the English Civil War. his supporters were…

Charles II

His becoming of kind of England was known as the Restoration s…

continuous limit

preservation of sign lemma 2

limits and continuity

algebra of continuous limits

f : (a, b)\{c} →

**R**... we say that f(x) tends to α as x tends to…Suppose that c ∈ (a, b) and lim(x → c) f(x) = α > 0... then ∃ δ >…

c ∈ (a, b) and f : (a, b) →

**R**... then f is cts at c IFF lim(x →…f(x) → α and g(x) → β as x → c... then as x → c... (i) (f + g)(x) →…

continuous limit

f : (a, b)\{c} →

**R**... we say that f(x) tends to α as x tends to…preservation of sign lemma 2

Suppose that c ∈ (a, b) and lim(x → c) f(x) = α > 0... then ∃ δ >…

Ferdinand involved Germany in Italian a…

The Hapsberg family, in the 16th centur…

German affairs became chaotic during th…

Which side did Louis XIII's Cardinal Ri…

Hapsbergs

Austria; Bohemia; Hungary; Spain; Naples; Milan; Sicily; Ameri…

Augsberg

Bohemian nobles

Ferdinand involved Germany in Italian a…

Hapsbergs

The Hapsberg family, in the 16th centur…

Austria; Bohemia; Hungary; Spain; Naples; Milan; Sicily; Ameri…

sequence vs. series

how to find terms of a sequence easily…

arithmetic sequence *two important form…

geometric sequence *two important formu…

The series is the sum of the values of a sequence.

Enter the first term into your calculator. Then apply the form…

(1) nth term of arithmetic sequence: t1 + (n-1)*d, where d is…

(1) nth term: t1 * r^(n-1), where r is the common ratio and t1…

sequence vs. series

The series is the sum of the values of a sequence.

how to find terms of a sequence easily…

Enter the first term into your calculator. Then apply the form…

Average Rate Of Change

Relationship between AROC and IROC:

Calculus Concept of IROC

Geometric Meaning of IROC

(f(b)-f(a))/(b-a); slope of secant line

limit of AROC=IROC

derivative

Slope of Curve

Average Rate Of Change

(f(b)-f(a))/(b-a); slope of secant line

Relationship between AROC and IROC:

limit of AROC=IROC

Antiderivative

Representation of Antiderivatives

Antidifferentiation

C

A function F is an antiderivative of f on an interval I if F'(…

If F is an antiderivative of f on an interval I, then G is an…

Reverse differentiation (y = ∫f(x)dx = F(x) + C

∫0dx=?

Antiderivative

A function F is an antiderivative of f on an interval I if F'(…

Representation of Antiderivatives

If F is an antiderivative of f on an interval I, then G is an…

What is the derivative of 10x³

When taking the antiderivative of a fun…

When evaluating a finite integral, what…

What is done when a function is integra…

30x²

+C

Integrate the function ∫ at the upper limit minus the lower fu…

Take the antiderivative of the function

What is the derivative of 10x³

30x²

When taking the antiderivative of a fun…

+C

The definite integral as the area of a…

Continuity implies integrability

Michelle Ott

Area of a trapezoid

Area= the integral from a to b of f(x) dx

If a function f is continuous on the closed interval [a,b], th…

The Best AP Statistics Teacher, The Best AP Calculus BC Teache…

(1/2)h x (b1+b2)

The definite integral as the area of a…

Area= the integral from a to b of f(x) dx

Continuity implies integrability

If a function f is continuous on the closed interval [a,b], th…

definition of continuity

limit does not exist

Intermediate Value Theorem

definition of a derivative

1. lim x→c f(x) exists.... 2. f(c) exists.... 3. lim x→c f(x) = f(c)

1. f(x) approaches a different number from the right as it doe…

If f is continuous on the closed interval [a,b] and k is any n…

lim h→0 (f(x+h) - f(x)) / h

definition of continuity

1. lim x→c f(x) exists.... 2. f(c) exists.... 3. lim x→c f(x) = f(c)

limit does not exist

1. f(x) approaches a different number from the right as it doe…