# Shared Flashcard Set

## Details

AP Calculus - AP Exam Review
Math Facts for the AB Calculus exam
71
Mathematics
03/25/2009

Term
 sin(π/6)
Definition
 √32
Term
 The derivative of sin-1x
Definition
 1/√(1-x2)
Term
 cos(π/4)
Definition
 √(2)/2
Term
 sin(-π/3)
Definition
 -√(3)/2
Term
 tan x
Definition
 (sin x)/(cos x)
Term
 ln e6
Definition
 6
Term
 2log27
Definition
 7
Term
 The derviative of csc x
Definition
 -cscxcotx
Term
 The limit as x approaches 0 of(sin x)/x
Definition
 1
Term
 The Pythagorean Identity
Definition
 sin2x + cos2x = 1
Term
 The derivative of cot x
Definition
 -csc2x
Term
 The derivative of ax
Definition
 axlna
Term
 The derivative of f/g
Definition
 (gf'-fg')/g2
Term
 sin (2π/3)
Definition
 √(3)/2
Term
 The derivative of f(g(x))
Definition
 f'(g(x))g'(x)
Term
 The limit as x approaches ∞ of1/x
Definition
 0
Term
 cot(π/4)
Definition
 1
Term
 the derivative of tan x
Definition
 sec2x
Term
 cos(a + b)
Definition
 cosacosb - sinasinb
Term
 The derivative of cos-1x
Definition
 -1/√(1-x2)
Term
 The derivative of logbx
Definition
 1/(xlnb)
Term
 The derivative of cos x
Definition
 -sin x
Term
 tan(5π/2)
Definition
 undefined
Term
 Intermediate Value Theorem
Definition
 If f(x) is continuous on the closed interval [a,b], then for any k between f(a) and f(b), there exists c between a and b, such that f(c)=k.
Term
 sin(7π/4)
Definition
 -√(2)/2
Term
 The derivative of ln x
Definition
 1/x
Term
 Limit Definition of the derivative
Definition
 The limit as h approaches 0 of(f(x+h)-f(x))/h
Term
 ln 1
Definition
 0
Term
 sin(a + b)
Definition
 sinacosb + cosasinb
Term
 cos (0)
Definition
 1
Term
 The derivative of sec x
Definition
 secxtanx
Term
 tanπ
Definition
 0
Term
 The limit as x approaches 0 of1/x
Definition
 Does not exist.
Term
 cos(π/2)
Definition
 0
Term
 The derivative of fg
Definition
 f'g+fg'
Term
 The derivative of ex
Definition
 ex
Term
 tan-1(1)
Definition
 π/4
Term
 The derivative of tan-1x
Definition
 1/(1+x2)
Term
 arccos(0.5)
Definition
 π/3
Term
 sin-1x represents...
Definition
 the angle between -π/2 and π/2 inclusive whose sine is x.
Term
 cos-1x represents...
Definition
 the angle between 0 and π inclusive whose cosine is x.
Term
 tan-1x represents...
Definition
 the angle between -π/2 and π/2 whose tangent is x.
Term
 logba represents...
Definition
 the exponent needed to raise b to get a.
Term
 log232
Definition
 5
Term
 log(1/100)
Definition
 -2
Term
 ∫sinx dx
Definition
 -cos x + C
Term
 ∫cos x dx
Definition
 sin x + C
Term
 ∫secxtanx dx
Definition
 sec x + C
Term
 ∫sec2x dx
Definition
 tan x + C
Term
 ∫csccotx dx
Definition
 -csc x + C
Term
 ∫csc2x dx
Definition
 -cotx + C
Term
 ∫ex dx
Definition
 ex + C
Term
 ∫e7x dx
Definition
 (1/7)e7x + C
Term
 ∫x-1 dx
Definition
 ln |x| + C
Term
 ∫(1/(1+x2) dx
Definition
 tan-1x + C
Term
 ∫ax dx
Definition
 (1/ln a)ax + C
Term
 The conditions for the Mean Value Theorem
Definition
 f(x) must be continuous on the closed interval [a,b] and differentiable on the open interval (a,b).
Term
 The conclusion of the Mean Value Theorem
Definition
 There exists c in (a,b) such that f'(c) = (f(b)-f(a))/(b-a)
Term
 The average value of a function on an interval [a,b].
Definition
 1/(b-a)∫f(x)dx (The def. integral from a to b)
Term
 The average rate of change of a function, f(x), on an interval [a,b].
Definition
 (f(b)-f(a))/(b-a)
Term
 The area of a circle
Definition
 πr2
Term
 The volume of a "shell"
Definition
 2πrhdx (or dy)
Term
 Area of a Washer
Definition
 π(R2-r2)
Term
 The Fundamental Theorem of Calculus
Definition
 ∫f(x) dx from a to b = F(b)-F(a) where F'(x)=f(x)  *I don't have the ability to write the boundaries on a def. integral.
Term
 Even Function
Definition
 f(-x)=f(x) Also is symmetric about y-axis
Term
 Odd Function
Definition
 f(-x)=-f(x) Also is symmetric about the origin.
Term
 ∫f(x) dx from -a to a where f(x) is odd
Definition
 ZERO!
Term
 ∫f(x) dx from -a to a where f(x) is even
Definition
 2∫f(x) dx from 0 to a
Term
 ∫af(x) dx
Definition
 a∫f(x) dx
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