Pre-Calc Homework Solutions 66

Pre-Calc Homework Solutions 66 - 66 Chapter 2 Review 13...

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Chapter 2 Review Exercises (pp. 91–93) 1. lim x 2 2 ( x 3 2 2 x 2 1 1) 5 ( 2 2) 3 2 2( 2 2) 2 1 1 52 15 2. lim x →-2 } 3 x 2 x 2 2 1 2 x 1 1 5 } 5 5 } 2 5 1 } 3. No limit, because the expression ˇ 1 w 2 w 2 w x w is undefined for values of x near 4. 4. No limit, because the expression ˇ 4 9 w 2 w x w 2 w is undefined for values of x near 5. 5. lim x 0 5 lim x 0 } 2 2 2 x (2 (2 1 1 x ) x ) } 5 lim x 0 } 2 x (2 2 1 x x ) } 5 lim x 0 1 2 } 2(2 1 1 x ) } 2 5 2 } 2(2 1 1 0) } 5 2 } 1 4 } 6. lim x 6‘ } 2 5 x x 2 2 1 1 3 7 } 5 lim x 6‘ } 2 5 x x 2 2 } 5 } 2 5 } 7. An end behavior model for } 12 x x 4 3 1 1 x 1 3 28 } is } 1 x 2 4 x 3 } 5 } 1 1 2 } x . Therefore: lim x } 12 x x 4 3 1 1 x 1 3 28 } 5 lim x } 1 1 2 } x 5 ‘ lim x 2‘ } 12 x x 4 3 1 1 x 1 3 28 } 5 lim x 2‘ } 1 1 2 } x 5 2‘ 8. lim x 0 } sin 4 x 2 x } 5 } 1 2 } lim x 0 } sin 2 x 2 x } 5 } 1 2 } (1) 5 } 1 2 } 9. Multiply the numerator and denominator by sin x . lim x 0 } x c x sc cs x c 1 x 1 } 5 lim x 0 } x 1 x sin x } 5 lim x 0 1 1 1 } sin x x } 2 5 1 lim x 0 1 2 1 1 lim x 0 } sin x x } 2 5 1 1 1 5 2 10. lim x
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