ab calc memorization Flashcards
1
Q
tanx =
A
sin x / cos x
2
Q
tan^2 x
A
= sec^2 x - 1
3
Q
definition of continuity
A
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+
4
Q
speed
A
absolute value of v(t)
5
Q
regular mean value theorem
A
must be continuous on [a,b] and differentiator on (a,b)
f’(c) = f(b)-f(a)/ b-a
6
Q
average rate of change
A
f(b)-f(a)/b-a
slope between two points
7
Q
instantaneous rate of change
A
f’(c) slope at a single point
8
Q
extreme value theorem
A
a function f that is continuous on [a,b] and has both an absolute min and absolute max
9
Q
derivative sin x
A
cos x
10
Q
derivative cos x
A
-sin x
11
Q
derivative tan x
A
sec^2 x
12
Q
derivative for cot x
A
-csc^2 x
13
Q
derivative sec x
A
sec x tan x
14
Q
derivative csc x
A
-csc x cot x
15
Q
derivative of arc sin x
A
1/square root(1-x^2)
