1013_su11_lec1_questions

1013_su11_lec1_questions - (8) w p z +1 x/y P = ± w z + 1...

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TAKING x, y, z, w, a, b, c, d BELOW TO BE ANY NUMBERS FOR WHICH THE THE EXPRESSIONS ON BOTH SIDES OF THE EQUATION IN QUESTION ARE DEFINED, DETERMINE WHICH OF THE FOLLOWING EQUATIONS ARE TRUE IN ALL SUCH CIRCUMSTANCES (1) x + ( y + z ) = ( x + y ) + z (2) x - ( y - z ) = ( x - y ) - z (3) ( a + b + c + d )( x + y + z + w ) = ax + by + cz + dw + ay + bx + cw + dz (4) x p y z P = xy z (5) 3 x + y = 3 x + 3 y (6) x + y z = x z + y z (7) z + w x + y = z x + w y (8) w p z +1 x/y P = ± w z + 1 ² p y x P (9) 16 5 / 4 = 32 (10) 2 - 2 = - 4 (11) ± 1 27 ² - 2 / 3 = - 1 / 9 (12) More generally, if x, y are both > 0 , x - y < 0 (13) x + y = x + y (14) 1 x + 4 = 1 x + 1 2 (15) e x = ( e ) x (16) sin (2 x ) x = sin (2) (17) sin ( x + y ) = sin ( x ) + sin ( y ) (18) cos ( xy ) = cos ( x ) cos ( y ) (19) tan ± x y ² = tan ( x ) tan ( y ) (20) e x + y = e x + e y (21) ℓn ( x 2 + 4) = ℓn ( x 2 ) + ℓn (4) (22) sin p π 4 ℓn ( e 2 ) P = 1
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ANSWERS (Correct in red, all others false) (1) x + ( y + z ) = ( x + y ) + z (2) x - ( y - z ) = ( x - y ) - z (3) ( a + b + c + d )( x + y + z + w ) = ax + by + cz + dw + ay + bx + cw + dz (4) x p y z P = xy z (5) 3 x + y = 3 x + 3 y (6) x + y z = x z + y z (7) z + w x + y = z x + w y
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Unformatted text preview: (8) w p z +1 x/y P = ± w z + 1 ² p y x P (9) 16 5 / 4 = 32 (10) 2-2 =-4 (11) ± 1 27 ²-2 / 3 =-1 / 9 (12) More generally, if x, y are both > , x-y < (13) √ x + y = sqrtx + √ y (14) 1 √ x + 4 = 1 √ x + 1 2 (15) √ e x = ( √ e ) √ x (16) sin (2 x ) x = sin (2) (17) sin ( x + y ) = sin ( x ) + sin ( y ) (18) cos ( xy ) = cos ( x ) cos ( y ) (19) tan ± x y ² = tan ( x ) tan ( y ) (20) e x + y = e x + e y (21) ℓn ( x 2 + 4) = ℓn ( x 2 ) + ℓn (4) (22) sin p π 4 ℓn ( e 2 ) P = 1...
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This note was uploaded on 09/04/2011 for the course MATH 1013 taught by Professor Zeto during the Summer '10 term at York University.

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1013_su11_lec1_questions - (8) w p z +1 x/y P = ± w z + 1...

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