Algebra and trigonometry 4e by stewart 1

geometric formulas exponents and radicals m x x m2n xn x 2n n x x n xn a b n y y x m x n 5 x m1n x m n  5 x mn n n n xy2  5 x y n x 1/n ! x n n n n ! xy ! x! y m n n m Formulas for area A, perimeter P, circumference C, volume V: Rectangle Box A 5 l„ V 5 l„ h P 5 2l 1 2„ n x m/n !x m !x2 m n x ! x n Åy !y n mn " !x " ! x ! x special products x 1 y 2 5 x 2 1 2x y 1 y x 2 y 2 5 x 2 2 2x y 1 y h „ Triangle Pyramid A 5  12 bh V 5 13 x 1 y 3 5 x 3 1 3x y  1 3x y 2 1 y h x 2 y 3 5 x 3 2 3x y  1 3x y 2 2 y FACtORING formulas x 2 2 y 2 5  x 1 y x 2 y x 2 1 2xy 1 y 2 5  x 1 y 2 2 x  2 2xy 1 y  5  x 2 y 2 x 3 1 y 3 5  x 1 y x 2 2 xy 1 y 2 x 3 2 y 3 5  x 2 y x 2 1 xy 1 y 2 „ l l h a a b Circle Sphere V 5 43 pr A 5 pr C 5 2pr A 5 4pr r r QUADRATIC FORMULA If ax 2 1 bx 1 c 5 0, then x5 2b "b 2 4ac 2a inequalities and absolute value Cylinder Cone V 5 pr 2h V 5 31 pr 2h r h h r If a , b and b , c, then a , c If a , b, then a 1 c , b 1 c If a , b and c . 0, then ca , cb If a , b and c , 0, then ca . cb heron’s formula If a . 0, then x  5 a  means  x 5 a  or  x 5 2a x  , a  means  2a , x , a x  . a  means  x . a  or  x , 2a B Area 5 !s1s a2 1s b2 1s c2 a1b1c where s c A a b C Copyright 2016 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it distance and midpoint formulas Graphs of Functions Distance between P1 x , y and P2 x , y 2 : Linear functions:   f1x2 mx b y d "1 x2 x1 2 1y2 y1 2 Midpoint of P1P2:   a lines x1 x2 y1 y2 , b 2 y b b x x Ï=b y2 y1 m5 x2 x1 Slope of line through P1 x , y and P2 x , y 2      Ï=mx+b Power functions:   f1x2 x n y 2 y 1 5 m x 2 x Point-slope equation of line through P1 x 1, y with slope m Slope-intercept equation of line with slope m and y-intercept b y 5 m x 1 b Two-intercept equation of line with x-intercept a and y-intercept b y x 51 a b y y x x Ï=≈      n Root functions:   f1x2 ! x logarithms y y y 5 log a x  means  a y 5 x Ï=x£ a log a x 5 x log a a x 5 x log a 1 5 0 log a a 5 1 x x log x 5 log 10 x ln x 5 log e x log a a}x}b 5 log a x  2 log a y y loga x log a x b 5 b log a x log b x 5  loga b Ï=œ∑ x log a x y 5 log a x 1 log a y      Ï=£œx ∑ Reciprocal functions:   f1x2 1/x n y y exponential and logarithmic functions y y y=a˛ a>1 y Ï= x y y=log a x a>1 x x y=a˛ 0