Pre-Calc Homework Solutions 42

Pre-Calc Homework Solutions 42 - lim x 2 2 G ( x ) 5 1 (b)...

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Chapter 2 Limits and Continuity Section 2.1 Rates of Change and Limits (pp. 55–65) Quick Review 2.1 1. f (2) 5 2(2 3 ) 2 5(2) 2 1 4 5 0 2. f (2) 5 } 4( 2 2 3 ) 2 1 2 4 5 } 5 } 1 1 1 2 } 3. f (2) 5 sin 1 p ? } 2 2 } 2 5 sin p 5 0 4. f (2) 5 } 2 2 1 2 1 } 5 } 1 3 } 5. ) x ) , 4 2 4 , x , 4 6. ) x ) , c 2 2 c 2 , x , c 2 7. ) x 2 2 ) , 3 2 3 , x 2 2 , 3 2 1 , x , 5 8. ) x 2 c ) , d 2 2 d 2 , x 2 c , d 2 2 d 2 1 c , x , d 2 1 c 9. } x 2 2 x 3 1 x 2 3 18 } 5 } ( x 1 x 3 1 )( x 3 2 6) } 5 x 2 6, x ±2 3 10. } 2 x 2 2 x 1 2 2 x 2 x 1 } 5 } (2 x x 2 (2 x 1) 2 ( x 1 1 ) 1) } 5 } x 1 x 1 } , x ± } 1 2 } Section 2.1 Exercises 1. (a) lim x 3 2 f ( x ) 5 3 (b) lim x 3 1 f ( x ) 5 –2 (c) lim x 3 f ( x ) does not exist, because the left- and right-hand limits are not equal. (d) f (3) = 1 2. (a) lim t 2 4 2 g ( t ) 5 5 (b) lim t 2 4 1 g ( t ) 5 2 (c) lim t 2 4 g ( t ) does not exist, because the left- and right-hand limits are not equal. (d) g ( 2 4) 5 2 3. (a) lim h 0 2 f ( h ) 52 4 (b) lim h 0 1 f ( h ) 52 4 (c) lim h 0 f ( h ) 5 –4 (d) f (0) 52 4 4. (a) lim s 2 2 2 p ( s ) 5 3 (b) lim s →- 2 1 p ( s ) 5 3 (c) lim s 2 2 p ( s ) 5 3 (d) p ( 2 2) 5 3 5. (a) lim x 0 2 F ( x ) 5 4 (b) lim x 0 1 F ( x ) 5 –3 (c) lim x 0 F ( x ) does not exist, because the left- and right-hand limits are not equal. (d) F (0) 5 4 6. (a)
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Unformatted text preview: lim x 2 2 G ( x ) 5 1 (b) lim x 2 1 G ( x ) 5 1 (c) lim x 2 G ( x ) 5 1 (d) G (2) 5 3 7. lim x 2 1/2 3 x 2 (2 x 2 1) 5 3 1 2 } 1 2 } 2 2 3 2 1 2 } 1 2 } 2 2 1 4 5 3 1 } 1 4 } 2 ( 2 2) 5 2 } 3 2 } Graphical support: [ 2 3, 3] by [ 2 2, 2] 8. lim x 2 4 ( x 1 3) 1998 5 ( 2 4 1 3) 1998 5 ( 2 1) 1998 5 1 Graphical support: [ 2 4.001, 2 3.999] by [0, 5] 9. lim x 1 ( x 3 1 3 x 2 2 2 x 2 17) 5 (1) 3 1 3(1) 2 2 2(1) 2 17 5 1 1 3 2 2 2 17 5 2 15 Graphical support: [ 2 3, 3] by [ 2 25, 25] 42 Section 2.1...
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This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Spring '08 term at University of Florida.

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