Business Calc Homework w answers_Part_11

Business Calc Homework w answers_Part_11 - Section 2.2 9....

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9. [ 2 2, 6] by [ 2 1, 5] lim x 2 1 } x 2 1 2 }5‘ 10. [ 2 2, 6] by [ 2 3, 3] lim x 2 2 } x 2 x 2 }52‘ 11. [ 2 7, 1] by [ 2 3, 3] lim x 2 3 2 } x 1 1 3 12. [ 2 7, 1] by [ 2 3, 3] lim x 2 3 1 } x 1 x 3 13. [ 2 4, 4] by [ 2 3, 3] lim x 0 1 } in x t x } 5 0 14. [ 2 4, 4] by [ 2 3, 3] lim x 0 2 } in x t x 15. [ 2 3, 3] by [ 2 3, 3] lim x 0 1 csc x 5‘ 16. [ 2 p , p ] by [ 2 3, 3] lim x ( p /2) 1 sec x 52‘ Section 2.2 51
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17. [ 2 4, 4] by [ 2 3, 3] (a) x 52 2, x 5 2 (b) Left-hand limit at 2 2 is . Right-hand limit at 2 2 is 2‘ . Left-hand limit at 2 is 2‘ . Right-hand limit at 2 is . 18. [ 2 7, 5] by [ 2 5, 3] (a) x 2 (b) Left-hand limit at 2 2 is 2‘ . Right-hand limit at 2 2 is . 19. [ 2 6, 6] by [ 2 12, 6] (a) x 1 (b) Left-hand limit at 2 1 is 2‘ . Right-hand limit at 2 1 is . 20. [ 2 2, 4] by [ 2 2, 2] (a) x 52} 1 2 } , x 5 3 (b) Left-hand limit at 2} 1 2 } is . Right-hand limit at 2} 1 2 } is 2‘ . Left-hand limit at 3 is . Right-hand limit at 3 is 2‘ . 21. [ 2 2 p ,2 p ] by [ 2 3, 3] (a) x 5 k p , k any integer (b) at each vertical asymptote: Left-hand limit is 2‘ . Right-hand limit is . 22. [ 2 2 p p ] by [ 2 3, 3] (a) x 5 } p 2 } 1 n p , n any integer (b) If n is even: Left-hand limit is . Right-hand limit is 2‘ . If n is odd: Left-hand limit is 2‘ . Right-hand limit is . 23. y 5 1 2 2 } x 1 x 1 } 2 1 } 5 1 x 2 x 2 } 2 5 1 } 2( x x 1 1 1) 1 2 x } 21 } 5 1 x 2 x 2 } 2 5 1 } x x 1 1 2 1 } 21 } 5 1 x 2 x 2 } 2 5 } x 3 1 x x 3 2 1 1 2 5 x x 2 1 5 } An end behavior model for y is } x x 3 3 } 5 1. lim x y 5 lim x 1 5 1 lim x 2‘ y 5 lim x 2‘ 1 5 1 24. y 5 1 } 2 x } 1 1 21 } 5 x 2 x 2 2 1 } 2 5 1 } 2 1 x x } 21 } 5 x 2 x 2 2 1 } 2 5 An end behavior model for y is } 5 x x 3 3 } 5 5. lim x y 5 lim x 5 5 5 lim x 2‘ y 5 lim x 2‘ 5 5 5 25. Use the method of Example 10 in the text. lim x 5 lim x 0 1 } 1 co 1 s x x } 5 } c 1 os 1 (0 0 ) } 5 } 1 1 } 5 1 lim x 2‘ 5 lim x 0 2 } 1 co 1 s x x } 5 } c 1 os 1 (0 0 ) } 5 } 1 1 } 5 1 26. Note that y 5 } 2 x 1 x sin x }5 2 1 } sin x x } . So, lim x y 5 lim x 2 1 lim x } sin x x } 5 2 1 0 5 2. Similarly, lim x 2‘ y 5 2. cos 1 } 1 x } 2 } 1 1 } 1 x } cos 1 } 1 x } 2 } 1 1 } 1 x } 5 x 3 1 10 x 2 2 x 2 2 }}} x 3 52 Section 2.2
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27. Use y 5 } 2 x s 2 in 1 x x } 5 } sin x x } ? } 2 x 1 1 1 } lim x 6‘ } sin x x } 5 0 lim x 6‘ } 2 x 1 1 1 } 5 0 So, lim x y 5 0 and lim x 2‘ y 5 0.
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This document was uploaded on 10/31/2011 for the course MAC 2311 at University of Florida.

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Business Calc Homework w answers_Part_11 - Section 2.2 9....

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