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review0 - Review for beginning of Math 242 This document...

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Review for beginning of Math 242 This document covers some topics that you should have learned in Math 241 or whatever your equivalent course was. If x = 3, evaluate x 2 , - x 2 , 2 x 2 , and - 2 x 2 . If x = - 3, evaluate x 2 , - x 2 , 2 x 2 , and - 2 x 2 . Expand and simplify: ( a + b )( x - y + z ) = ( a + b )( a - b ) = ( a + b )( a 2 - ab + b 2 ) = ( a + b )( a - b ) = 2 - 3 2 + 3 · 2 - 3 2 - 3 = ( x 2 + x - x ) · x 2 + x + x x 2 + x + x = Be very aware that a + b is VERY DIFFERENT from a + b ( a + b ) 2 is VERY DIFFERENT from a 2 + b 2 sin( a + b ) is VERY DIFFERENT from sin a + sin b ‘n ( a + b ) is VERY DIFFERENT from ‘n a + ‘n b Play around with this to convince yourself! Try some “nice” numbers, like a = 1 and b = 1. (For the sine function, examples of “nice” numbers might be a = π/ 2 and b = π/ 2.) 1
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Solve the inequalities. In other words, for each inequality, find all values of x that make the inequality true. x 2 < 9 x 2 > 9 | x - 3 | < 2 | x - 3 | > 2 Sketch the graphs of each of the following. y = x 2 x 2 + y 2 = 4 x 2 + y 2 = 2 y = x 2 / 3 x = y 2 / 3 Where does y = 1 + x intersect y = 1 + x 2 ?
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