Use LEFT and RIGHT arrow keys to navigate between flashcards;
Use UP and DOWN arrow keys to flip the card;
H to show hint;
A reads text to speech;
40 Cards in this Set
- Front
- Back
|
Definition of e |
e=lim(x>inf) (1+1/x)^x |
|
|
Defn of Derivative 1 |
|
|
|
Defn of Derivative 2 |
|
|
|
Rate of Change formula |
|
|
|
Rolle's Theorem |
If f is continuous on [a,b] + differentiable on (a,b) and f(a)=f(b), at least one c exists such that f'(c)=0 |
|
|
MVT |
If y=f(x) is cont. on [a,b] and differentiable at all points than at least one c exists such that f'(c)=[rate of change] |
|
|
IVT for functions |
A function y=f(x) that's cont. on [a,b] taks on every y-value from f(a) to f(b) |
|
|
IVT for derivatives |
If a and b are only 2 points in a differentiable interval, than f' takes on all values |
|
|
sin 2x |
2sinxcosx |
|
|
cos 2x |
cos^2 x-sin^2 x 2cos^2 x 1-2sin^2 x |
|
|
cos^2 x |
(1/2)(1-cos2x) |
|
|
sin^2 x |
(1/2)(1+cos2x) |
|
|
Defn of critical # |
A point in the interior of the domain of a function f at which f'=0 or f' does not exist |
|
|
First derivative test |
f' goes + to - (- to +) then c is max (min) f'<0 (f'>0) for x>a and a is left endpt then a is max(min) f'<0 (f'>0) for x |
|
|
second derivative test |
When f'(c)=0: f"(c)<0, then c is max f"(c)>0, then c is min |
|
|
Concavity |
CCD if y' is decreasing CCU if y' is increasing |
|
|
test for concavity |
slope changes + to - (- to +) ccd (ccu) f"<0 (f">0) |
|
|
Defn of inflection point |
Point on graph with tangent line and change in concavity |
|
|
Linearization |
L(x)=f(a)+f'(a)(x-a) |
|
|
Newtons Method |
|
|
|
Defn of Differentials |
If y=f(x) is a diff function, the diff dx is an independent variable and the diff dy is dy=f'(x)dx |
|
|
Fundamental Theorem of Calc I and II |
|
|
|
Eulers Method |
Chart Such as: (x,y) x change dy/dx y change (x,y)new |
|
|
Carrying Capacity |
K=P(1+Ae^(kt)) |
|
|
general Logistic formula |
dP/dt=kP(1-P/k) |
|
|
Average vaue of f(x) |
|
|
|
Volume by discs |
|
|
|
Volume by washers |
(instead of x^2: X^2-x^2) |
|
|
Volume by cross sections |
integral from a to b of (area of section)dx |
|
|
Object with position s(t) |
velocity= s'(t) speed= |v(t)| Acc=v'(t) Displacement= integral a to b v(t)dt Distance= integral a to b |v(t)|dt |
|
|
Integration by parts |
|
|
|
arc length of function |
|
|
|
Object along curve |
Position <x(t),y(t)> velocity <x'(t),y'(t)> Acc <x"(t),y"(t)> Magnitude |s(t)| Arc Length Int a to b of |s(t)| |
|
|
Polar Curve Formulas |
x=rcos@ y=rsin@ slope=(dy/d@)/(dx/d@) |
|
|
Area of Polar Curves |
|
|
|
Know MacLaurin Series! |
Know THEM! |
|
|
Remainder Estimation Theorem |
R=((f(n+1))/(n+1)!)x(x-c)^(n+1) |
|
|
lim(x to 0) sinx/x |
1 |
|
|
lim(x to inf) sinx/x |
0 |
|
|
L'Hopital's rule |
|
