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AP Calculus - AP Exam Review
Math Facts for the AB Calculus exam
71
Mathematics
12th Grade
03/25/2009
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Term
sin(π/6)
 Definition
√3
2
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 ∞ of

1/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 of

1/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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