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Pre-Calc Homework Solutions 45

# Pre-Calc Homework Solutions 45 - Section 2.1 31(a True(b...

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31. (a) True (b) True (c) False, since lim x 0 2 f ( x ) 5 0. (d) True, since both are equal to 0. (e) True, since (d) is true. (f) True (g) False, since lim x 0 f ( x ) 5 0. (h) False, lim x 1 2 f ( x ) 5 1, but lim x 1 f ( x ) is undefined. (i) False, lim x 1 1 f ( x ) 5 0, but lim x 1 f ( x ) is undefined. (j) False, since lim x 2 2 f ( x ) 5 0. 32. (a) True (b) False, since lim x 2 f ( x ) 5 1. (c) False, since lim x 2 f ( x ) 5 1. (d) True (e) True (f) True, since lim x 1 2 f ( x ) ± lim x 1 1 f ( x ). (g) True, since both are equal to 0. (h) True (i) True, since lim x c f ( x ) 5 1 for all c in (1, 3). 33. y 1 5 } x 2 x 1 2 x 1 2 2 } 5 } ( x 2 x 1 2 )( x 1 1 2) } 5 x 1 2, x ± 1 (c) 34. y 1 5 } x 2 x 2 2 x 1 2 2 } 5 } ( x 1 x 1 2 )( x 1 2 2) } (b) 35. y 1 5 } x 2 2 x 2 2 x 1 1 1 } 5 } ( x x 2 2 1 1 ) 2 } 5 x 2 1, x ± 1 (d) 36. y 1 5 } x 2 x 1 1 x 1 2 2 } 5 } ( x 2 x 1 1 )( x 1 1 2) } (a) 37. Since int x 5 0 for x in (0, 1), lim x 0 1 int x 5 0. 38. Since int x 52 1 for x in ( 2 1, 0), lim x 0 2 int x 1. 39. Since int x 5 0 for x in (0, 1), lim x 0.01 int x 5 0.
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