Logo

Go on. Explore!

lvl 0 • 0 xp

lvl 1

HomeMarketDecksInterests
AP Calculus Theorems

AP Calculus Theorems

memorize.aimemorize.ai (lvl 286)
Star 0%
Star 0%
Star 0%
Star 0%
Star 0%
(0)
(0)
(0)
17 cards
()
Section 1

Preview this deck

Fundamental Theorem of Calculus

Front

1 / 17

CalculusMath
Star 0%
Star 0%
Star 0%
Star 0%
Star 0%

0.0

0 reviews

5
0
4
0
3
0
2
0
1
0

Active users

0

All-time users

0

Favorites

0

Last updated

5 years ago

Date created

Mar 14, 2020

Cards (17)

Section 1

(17 cards)

Fundamental Theorem of Calculus

Front

The integral on (a, b) of f(x) dx = F(b) - F(a)

Back

Definition of a Derivative

Front

lim h→0 (f(x+h) - f(x)) / h

Back

Rolle's Theorem

Front

Let f be continuous on the closed interval [a, b] and differentiable on the open interval (a, b). If f(a) = f(b) then there is at least one number c in (a, b) such that f'(c)= 0

Back

Product Rule

Front

d/dx (f(x) g(x)) = f(x)g'(x) + g(x) f'(x)

Back

The first derivative gives what?

Front

1. critical points 2. relative extrema 3. increasing and decreasing intervals

Back

The second derivative gives what?

Front

1. points of inflection 2. concavity

Back

Quotient Rule

Front

d/dx (g(x)/ h(x)) = (h(x) g'(x) - g(x) h'(x))/ h(x)^2

Back

Chain Rule

Front

d/dx f(g(x)) = f'(g(x)) g'(x)

Back

Definition of Continuity

Front

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

Back

Extrema Value Theorem

Front

If f is continuous on the closed interval [a, b], then f has both a maximum and a minimum on the interval.

Back

Mean Value Theorem

Front

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

Back

Derivative of an Inverse Function

Front

g'(x) = 1/ f'(g(x)) where g(x) is the inverse of f(x)

Back

Mean Value Theorem (Integrals)

Front

The integral on (a, b) of f(x) dx = f(c) (b - a)

Back

Intermediate Value Theorem

Front

If f is continuous on the closed interval [a,b] and k is any number between f(a) and f(b) then there is at least one number c in [a, b] such that f(c) = k

Back

Second Fundamental Theorem of Calculus

Front

If f is continuous on an open interval containing a, then for every x in the interval the derivative of the the integral of f(x) dx on said interval is equal to f(x)

Back

When does the limit not exist?

Front

1. f(x) approaches a different number from the right as it does from the left as x→c 2. f(x) increases or decreases without bound as x→c 3. f(x) oscillates between two fixed values as x→c

Back

Average Value Theorem

Front

1/ (b-a) times the integral on (a, b) of f(x) dx

Back