ab calc memorization Flashcards
tanx =
sin x / cos x
tan^2 x
= sec^2 x - 1
definition of continuity
a function f that is continuous at an x value if and only if f(c) exists and is equal to lim f(x) x-> c- equals lim f(x) x-> c+
speed
absolute value of v(t)
regular mean value theorem
must be continuous on [a,b] and differentiator on (a,b)
f’(c) = f(b)-f(a)/ b-a
average rate of change
f(b)-f(a)/b-a
slope between two points
instantaneous rate of change
f’(c) slope at a single point
extreme value theorem
a function f that is continuous on [a,b] and has both an absolute min and absolute max
derivative sin x
cos x
derivative cos x
-sin x
derivative tan x
sec^2 x
derivative for cot x
-csc^2 x
derivative sec x
sec x tan x
derivative csc x
-csc x cot x
derivative of arc sin x
1/square root(1-x^2)
derivative arc tan x
1/1+x^2
e^-4x derivative
-4e^-4x
derivative 5e^x
5e^x
if f is defined at x=a then
∫a,a (f(x)) dx = 0
if ∫10,1 (f(x)) dx = 4 and ∫3,10 (f(x)) dx = 7
then ∫3,1 (f(x)) dx = (4)-(-7) = 11
