Studied by 146 peopleCalculus
Differential Equations
AP Calculus BC
Unit 1: Limits and Continuity
AP
Calculus BC
Review
Final
Images
Everything!
Everything
Equations
Theorems
Theories
Rules
Derivatives
Integrals
Slope
Distance
Displacement
Polar
Parametric
Cartesian
Average Value Theorem
Mean Value Theorem
Extreme Value Theorem
Continuity
Final Review
AP Test
11th
This includes a ton of stuff you must remember for the AP Test. It includes equations, theories, rules, derivatives, integrals, and more. I only recommend using these as flashcards or multiple choice only.
L'Hôpital's Rule
Slope of a Parametric equation
Euler’s Method
Polar Area
Polar Slope
Integration by parts
Integral of logarithms
Ratio Test
sin(2x)
2sin(x)cos(x)
cos(2x)
cos^2(x) - sin^2(x)
cos(2x)
1 - 2sin^2(x)
cos^2(x)
1/2(1+cos(2x))
sin^2(x)
1/2(1-cos(2x))
sin^2(x) + cos^2(x)
1
1+tan^2(x)
sec^2(x)
cot^2(x) + 1
csc^2(x)
sin(-x)
-sin(x)
cos(-x)
cos(x)
Taylor Series
f(x) = f(a) + f’(a)(x-a) + [f’’(a)(x-a)^2 / 2!] + [f’’’(a)(x-a)^3 / 3!] + …
Lagrange Error Bound
Maclaurin Series
Alternating Series Error Bound
Geometric Series
sin(0)
0
cos(0)
1
tan(0)
0
sin(pi/6)
1/2
cos(pi/6)
root3/2
sin(pi/4)
root2/2
cos(pi/4)
root2/2
sin(pi/3)
root3/2
cos(pi/3)
1/2
sin(pi/2)
1
cos(pi/2)
0
Chain Rule
Product Rule
Quotient Rule
Trapezoidal Rule
NEVER FORGET (for integrals)
+C
Average Value
d/dx sin(x)
cos(x)
d/dx cos(x)
-sin(x)
d/dx tan(x)
sec^2(x)
d/dx cot(x)
-csc^2(x)
d/dx sec(x)
sec(x)tan(x)
d/dx csc(x)
-csc(x)cot(x)
d/dx ln(u)
1/u
Solid Disk Method
Solid Washer Method
Cartesian Arc Length
Polar Arc Length
Parametric Arc Length
Intermediate Value Theorem
If the function f(x) is continuous on [a,b], then f(x) achieves every value between f(a) and f(b) in the open interval (a,b).
Mean Value Theorem
If the function f(x) continuous on [a,b], and the first derivative exists on the interval (a,b), then there is at least one number x = c in (a,b) such that f’(c) = [ f(b)-f(a) ] / (b-a).
Rolle’s Theorem
Same as mean value theorem but if f(a) = f(b), then there is at least one number x = c in (a,b) such that f’(c) = 0.
d/dx loga(x)
1/xln(a)
Displacement
Speed
Distance
![<p>If the function f(x) <mark data-color="yellow">continuous on [a,b], and the first derivative exists on the interval (a,b)</mark>, then there is at least one number x = c in (a,b) such that f’(c) = [ f(b)-f(a) ] / (b-a).</p>](https://knowt-user-attachments.s3.amazonaws.com/a559904ffac24820b04928c7ae6b6bda.jpeg)
Note
Flashcard