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basic things to remember
basic things for the final exam
81
Mathematics
Undergraduate 1
12/05/2013
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Term
distance formula
 Definition
√((x2-x1)2+(y2-y1)2)
Term
midpoint formula
 Definition
(((x1+x2)/2), ((y1+y2)/2)
Term
circle equation
 Definition
(x-h)2+(y-k)2=r2
Term
slope of a nonvertical line
 Definition

rise/run

 

(y2-y1)/(x2-x1)
Term
point-slope form
 Definition
[image]
Term
general form of a line
 Definition
ax+by+c=0
Term
identity function
 Definition
f(x)=x
Term
constant function
 Definition
f(x)=c
Term
squaring function
 Definition
f(x)=x2
Term
cubing function
 Definition
f(x)=x3
Term
absolute value function
 Definition
f(x)=|x|
Term
square root function
 Definition
[image]
Term
cube root function
 Definition
[image]
Term
reciprocal function
 Definition
f(x)=1/x
Term
reciprocal square function
 Definition
f(x)=1/x2
Term
rational power function
 Definition
f(x)=xm/n
Term
greatest integer function
 Definition
f(x)=[[x]]
Term
standard form of a quadratic function
 Definition
[image]
Term
simple interest formula
 Definition
i=prt
Term
future value for simple interest
 Definition
a(t)=p+prt
Term
compound interest
 Definition
[image]
Term
euler constant, e
 Definition
[image]
Term
continuous compounding
 Definition
a=pert
Term
product rule of logarithms
 Definition
[image]
Term
quotient rule of logarithms
 Definition
[image]
Term
power rule of logarithms
 Definition
[image]
Term
csc x
 Definition
1/sin x
Term
change-of-base formula
 Definition

logbx=

logax/logab (base a)

log x/log b (base 10)

ln x/ln b (base e)

 
Term
sec x
 Definition
1/cos x
Term
cot x
 Definition
1/tan x
Term
tan x
 Definition
sin x/cos x
Term
cot x
 Definition
cos x/sin x
Term
sin(-x)
 Definition
-sin x
Term
cos(-x)
 Definition
cos x
Term
tan (-x)
 Definition
-tan x
Term
csc(-x)
 Definition
-csc x
Term
sec(-x)
 Definition
sec x
Term
cot(-x)
 Definition
-cot x
Term
tan x
 Definition
sin x/cos x
Term
cot x
 Definition
cos x/sin x
Term
sin(-x)
 Definition
-sin x
Term
cos(-x)
 Definition
cos x
Term
tan (-x)
 Definition
-tan x
Term
csc(-x)
 Definition
-csc x
Term
sec(-x)
 Definition
sec x
Term
cot(-x)
 Definition
-cot x
Term
sin2x+cos2x
 Definition
1
Term
1+tan2x
 Definition
sec2x
Term
1+cot2x
 Definition
csc2x
Term
cos(u-v)
 Definition
cos u cos v + sin u sin v
Term
cos(u+v)
 Definition
cos u cos v - sin u sin v
Term
sin(u-v)
 Definition
sin u cos v - cos u sin v
Term
sin(u+v)
 Definition
sin u cos v + cos u sin v
Term
tan(u-v)
 Definition
(tan u − tan v) / (1 + tan u tan v)
Term
tan(u+v)
 Definition
(tan u + tan v) / (1 − tan u tan v)
Term
[image]
 Definition
[image]
Term
[image]
 Definition
[image]
Term
[image]
 Definition
[image]
Term
[image]
 Definition
[image]
Term
[image]
 Definition
[image]
Term
[image]
 Definition
sec x
Term
sin 2x
 Definition
2 sin x cos x
Term
cos 2x (1)
 Definition
cos2x-sin2x
Term
cos 2x (2)
 Definition
1-2 sin2x
Term
cos 2x (3)
 Definition
2 cos2x-1
Term
tan 2x
 Definition
(2 tan x)/(1-tan2x)
Term
[image]
 Definition
[image]
Term
[image]
 Definition
[image]
Term
[image]
 Definition
[image]
Term
[image]
 Definition
[image]
Term
[image]
 Definition
[image]
Term
[image]
 Definition
[image]
Term
[image]
 Definition
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Term
[image]
 Definition
[image]
Term
[image]
 Definition
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Term
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 Definition
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Term
[image]
 Definition
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Term
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 Definition
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Term
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 Definition
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Term
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 Definition
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