Math16Apexam1 - y-intercepts of the graph of y = x 3-x 2-2...

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Math 16A: Practice problems for Midterm 1 Note: The midterm itself will not be this long. These are just some problems to get you ready. Problem 1. Find the following limits. (a) lim x 1 (2 x 2 + 3 x - 1) (b) lim x →- 2 + x +3 x - 2 (c) lim x →- 2 x +3 x - 2 (d) lim t 0 - t 2 +2 t (e) lim Δ x 0 ( x x ) 2 - x 2 Δ x (f) lim x →∞ 4 x 3 + x - 1 x 2 +5 (g) lim x →∞ 7 x 2 x 3 - x 2 (h) lim x →-∞ 2 - x 2 x +1 (i) lim x →∞ 4 x 2 +5 x - 2 3 x 2 - x +1 2. Determine whether each equation defines y as a func- tion of x : (a) 2 x 2 + y = 3 (b) x 2 y 2 - 1 = 0 (c) xy - 3 y = 1 1
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3. Let f ( x ) = 1 x and g ( x ) = x 2 + 3 . Find the following: (a) f (1) (b) g ( 3) (c) f ( x + 1) (d) g (2 x ) (e) ( f g )( x ) (f) ( g f )( x ) (g) ( f f )( x ) 4. Find the distance between the points (1 , 4) and ( - 1 , 2) . 5. Find the midpoint of the line segment between the points (2 , 5) and (1 , - 4) . 6. Find the x -intercepts and
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Unformatted text preview: y-intercepts of the graph of y = x 3-x 2-2 x . 7. Find the points of intersection of the graphs of y = x 2 and y = x + 1 . 8. Find an equation for the line passing through the points (-1 , 5) and (2 , 3) . 9. Find the equation of the horizontal line passing through the point (1 ,-3) . 10. What is the center and radius of the circle ( x + 1) 2 + ( y-2) 2 = 9 ? 2 11. On which intervals are the following functions con-tinuous? (a) f ( x ) = x 2-2 x 2-9 (b) g ( x ) = x 3 +1 x-3 (c) h ( x ) = x x 2 +1 3...
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This note was uploaded on 06/23/2010 for the course MATH math16 taught by Professor Na during the Spring '10 term at UC Riverside.

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Math16Apexam1 - y-intercepts of the graph of y = x 3-x 2-2...

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