Review II spring 2011 L6 through L13 edited

Review II spring 2011 L6 through L13 edited - Review for...

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Review for MAC 1140 Exam 2 Spring 2011 1. Solve the following inequalities: (a) 2 x + 5 ± 4 + 3 x (b) ² 3 < 1 ² 2( x + 5) ± 5 (c) 2 + j 2 ² x j ³ 0 (d) 4 ² 8 3 j 2 x ² 3 4 + 1 2 j > 0 (ans: a. [1 ; 1 ), b. [ ² 7 ; ² 3), c. ( ²1 ; 1 ), d. ( ² 5 2 ; 7 2 ).) 2. Find x so that the distance between the points ( x; 3) and ( ² 3 ; 5) is 5. (ans: x = ² 3 ´ p 21) 3. Find the center C and radius r of the circle 3 x 2 + 3 y 2 + 12 x ² 6 y = 1. (ans: C ( ² 2 ; 1) and r = 4 p 3 3 ) 4. Find (a) the standard form and (b)the general form of the equations of the circle whose 2 end points of a diameter are (1 ; ² 2) ; (9 ; 6). (ans:( x ² 5) 2 + ( y ² 2) 2 = 32, x 2 ² 10 x + y 2 ² 4 y ² 3 = 0 ) 5. Find (a) the standard form and (b)the general form of the equations of the circle whose center is ( ² 1 ; ² 1) with radius 3. (ans:( x + 1) 2 + ( y + 1) 2 = 9 ;x 2 + 2 x + y 2 + 2 y ² 7 = 0 ) 6. Find (a) the standard form and (b)the general form of the equations of the circle with center (5 ; ² 3) passing through (1 ; 0). (ans:( x ² 5) 2 + ( y + 3) 2 = 25, and x 2 + 10 x + y 2 + 6 y + 9 = 0 ).
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7. Which of the following functions are even, odd or neither? Any symmetry? f ( x ) = j x ± 3 j ; g ( x ) = j x j ± 3 ; h ( x ) = x ± 3 ; p ( x ) = ( x ± 3) 2 + 3 ; q ( x ) = 1 p x 2 +5 ; k ( x ) = x 3 ± 2 x 2 ; l ( x ) = x 4 ± x 2 ; r ( x ) = x 3 + x 5 .
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Review II spring 2011 L6 through L13 edited - Review for...

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