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1013_su11_lec1_questions

# 1013_su11_lec1_questions - (8 w p z 1 x/y P = ± w z 1 ² p...

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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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