#### Study sets matching "ap calculus"

#### Study sets matching "ap calculus"

reverse chain rule

if integrating backwards

fundamental theorem of calculus

mean value theorem for integrals

substitute u

answer will be negative

if f is continuous on [a,b], then ∫f(x)dx = F(b) - F(a)

if f is continuous on [a,b] then there is at least one point X…

reverse chain rule

substitute u

if integrating backwards

answer will be negative

Copernicus (1473-1534)

Anton Van Leeuwenhoek (1632-1723)

Michel de Montaigne (1533-1592)

Francis Bacon (1561-1626)

heliocentric theory (sun is the center of solar system)

invented the microscope, introduced the science of microbiology

inventor of the essay, skeptic

created the experimental method, theory of empiricism - acquir…

Copernicus (1473-1534)

heliocentric theory (sun is the center of solar system)

Anton Van Leeuwenhoek (1632-1723)

invented the microscope, introduced the science of microbiology

1) Direct substitution ... 2) L'Hopital's…

Horizontal asymptotes

Use degrees and coefficients

Limit DNE

How to find finite (EX: x approaches 2) limits

Limits to ∞ are also called...

How to find limits to ∞

Limits to ∞: exponent is larger in numerator

1) Direct substitution ... 2) L'Hopital's…

How to find finite (EX: x approaches 2) limits

Horizontal asymptotes

Limits to ∞ are also called...

Intermediate Value Theorem (IVT)

Extreme Value Theorem

Fermat's Theorem

Rolle's Theorem

If f(x) is a continuous function on a closed interval [a,b], a…

If f(x) is continuous on a closed interval [a,b] then f(x) att…

If f(x) has a local maximum or minimum at c, and if f'(c) exis…

Let f(x) be a function that satisfies the following 3 hypothes…

Intermediate Value Theorem (IVT)

If f(x) is a continuous function on a closed interval [a,b], a…

Extreme Value Theorem

If f(x) is continuous on a closed interval [a,b] then f(x) att…

Find the Zeros

Find the equation of the line tangent t…

Find the equation of the line normal to…

Show that f(x) is even.

f(x)=0

Get x and y.... Get the slope at x.... y-y1=m(x-x1)

negative reciprocal.

f(x)=f(-x)

Find the Zeros

f(x)=0

Find the equation of the line tangent t…

Get x and y.... Get the slope at x.... y-y1=m(x-x1)

continuity

Indeterminate Forms of Limits

extreme value theorem

intermediate value theorem

when the limit of a function exists and the value exists and t…

0/0, ∞/∞, ∞+/-∞, 1^∞, 0^0

If f is continuous on a closed interval, then f has a max and…

if a<b and f(a) and f(b) are opposite signs then there must be…

continuity

when the limit of a function exists and the value exists and t…

Indeterminate Forms of Limits

0/0, ∞/∞, ∞+/-∞, 1^∞, 0^0

Nth term test

The s

Summation from n=1 to n=infinith of 1/n…

If there is an integer N such that uN>=…

If lim an=0, no conclusion can be made. If it doesn't, then it…

...

Series converges if p>1. Series diverges of p< or equal to 1

Series converges if un approches zero but diverges when un doe…

Nth term test

If lim an=0, no conclusion can be made. If it doesn't, then it…

The s

...

f is continuous at c if:

f is continuous on [a,b] if:

x = c is a vertical asymptote if and on…

y = c is a horizontal asymptote if and…

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

1. f is continuous on (a,b)... 2. lim f(x) = f(a)... x→a+... 3. lim f(…

lim f(x) = +-∞ ... x → c +-

lim f(x) = c... x→±∞

f is continuous at c if:

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

f is continuous on [a,b] if:

1. f is continuous on (a,b)... 2. lim f(x) = f(a)... x→a+... 3. lim f(…

Intermediate Value Theorem

Extreme Value Theorem

Rolle's Theorem

Mean Value Theorem

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

If f is continuous on [a,b], then f has both a minimum and a m…

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…

Intermediate Value Theorem

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

Extreme Value Theorem

If f is continuous on [a,b], then f has both a minimum and a m…

Disk Method

Washer Method (about the x-axis)

Washer Method (about the y-axis)

Washer Method (about a horizontal line)

-creates a solid... -area of each disk: 𝜋(f(x))²... -dx = thickness…

-creates a washer... -R = outer radius... -r = inner radius ... -area:…

-if bounded on the right by x = f(y) & on the left by x = g(y)…

1. limits of integration: set functions equal to each other... 2.…

Disk Method

-creates a solid... -area of each disk: 𝜋(f(x))²... -dx = thickness…

Washer Method (about the x-axis)

-creates a washer... -R = outer radius... -r = inner radius ... -area:…