College Algebra [4 ed.] 0534405991, 9780534405991
James Stewart, author of the worldwide, best-selling Calculus texts, along with two of his former Ph.D. students, Lothar
460 25 16MB
English Pages 817 Year 2003
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- Author / Uploaded
- James Stewart
- Lothar Redlin
- Saleem Watson
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EXPONENTS AND RADICALS
DISTANCE AND MIDPOINT FORMULAS
am amn an 1 an n a n an a n b b
aman amn ÓamÔn amn
Distance between P1Ó x 1, y 1Ô and P2Ó x 2, y 2Ô: 2 2 y d œÓ x x Ó y 2 1Ô 2 1Ô
Midpoint of P1 P2:
!@
ÓabÔn anbn a1n œn a
!œn a @ a mn œn am
2
1
2
m
œa a b œn b
n
1
LINES
n
œn b œn ab œn a
x x y y , @ ! 2 2
œm œn a œn œm a mœn a SPECIAL PRODUCTS ÓA BÔ2 A2 2AB B2
y2 y1 m x2 x1
Slope of line through P1Óx 1, y 1Ô and P2Óx 2, y 2Ô Point-slope equation of line through P1Óx 1, y 1Ô with slope m
y y 1 mÓ x x 1Ô
Slope-intercept equation of line with slope m and y-intercept b
y mx b x y 1 a b
Two-intercept equation of line with x-intercept a and y-intercept b
ÓA BÔ2 A2 2AB B2 ÓA BÔ3 A3 3A2B 3AB2 B3
The lines y m1 x b1 and y m 2 x b 2 are
ÓA BÔ3 A3 3A2B 3AB2 B3 FACTORING FORMULAS A2 B 2 ÓA BÔÓA BÔ
Parallel if the slopes are the same
m1 m2
Perpendicular if the slopes are negative reciprocals
m1 1m2
A2 2AB B2 ÓA BÔ2
LOGARITHMS
A2 2AB B2 ÓA BÔ2
y loga x
means a y x
A3 B 3 ÓA BÔÓA2 AB B2Ô
loga a x x
aloga x x
A B ÓA BÔÓA AB B Ô
loga 1 0
loga a 1
3
3
2
2
QUADRATIC FORMULA
Common and Natural Logarithms ln x loge x
log x log10 x
If ax 2 bx c 0, then a b œ b 2 4 c x 2a INEQUALITIES AND ABSOLUTE VALUE If a b and b c, then a c.
Laws of Logarithms loga AB loga A loga B A loga loga A loga B B
! @
loga AC C loga A
If a b, then a c b c. If a b and c 0, then ca cb.
Change of Base Formula
If a b and c 0, then ca cb.
loga x logb x loga b
If a 0, then x a
means x a
x a
means a x a.
x a
means x a
or
or
x a. x a.
SOME FUNCTIONS AND THEIR GRAPHS
y
y
y
fÓxÔ mx b
Linear functions
fÓxÔ ax
Exponential functions
Ï=a˛ a>1
y
Ï=a˛ 0