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Ap Calculus
Semester I Exam Review
104
Mathematics
12th Grade
12/02/2009
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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 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
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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
sin(7π/4)
 Definition
-√(2)/2
Term
The derivative of ln x
 Definition
1/x
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
∫ax dx
 Definition
(1/ln a)ax + C
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.

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∫af(x) dx
 Definition
a∫f(x) dx
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