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Pre-Calc Homework Solutions 57

# Pre-Calc Homework Solutions 57 - Section 2.3 19 sin x x 57...

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19. [ 2 3, 6] by [ 2 1, 5] (a) x 5 2 (b) Not removable, the one-sided limits are different. 20. [ 2 3, 6] by [ 2 1, 5] (a) x 5 2 (b) Removable, assign the value 1 to f (2). 21. [ 2 5, 5] by [ 2 4, 8] (a) x 5 1 (b) Not removable, it’s an infinite discontinuity. 22. [ 2 4.7, 4.7] by [ 2 3.1, 3.1] (a) x 52 1 (b) Removable, assign the value 0 to f ( 2 1). 23. (a) All points not in the domain along with x 5 0, 1 (b) x 5 0 is a removable discontinuity, assign f (0) 5 0. x 5 1 is not removable, the one-sided limits are different. 24. (a) All points not in the domain along with x 5 1, 2 (b) x 5 1 is not removable, the one-sided limits are different. x 5 2 is a removable discontinuity, assign f (2) 5 1. 25. For x ±2 3, f ( x ) 5 } x x 2 1 2 3 9 } 5 } ( x 1 x 3 1 )( x 3 2 3) }5 x 2 3. The extended function is y 5 x 2 3. 26. For x ± 1, f ( x ) 5 } x x 3 2 2 2 1 1 } 5 5 } x 2 x 1 1 x 1 1 1 } . The extended function is y 5 } x 2 x 1 1 x 1 1 1 } . 27. Since lim x 0 } sin x x } 5 1, the extended function is y 5 h 28. Since lim x 0 } sin x 4 x } 5 4 lim x 0 } sin 4 x 4 x } 5 4(1) 5 4, the extended function is y 5 h 29. For x ± 4 (and x . 0), f ( x ) 5 } ˇ x x w 2 2
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