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Pre-Calc Homework Solutions 54

Pre-Calc Homework Solutions 54 - 54 Section 2.2 1 x 47(a...

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47. (a) lim x 2‘ f ( x ) 5 lim x 2‘ 1 } 1 x } 2 5 0 (b) lim x f ( x ) 5 lim x ( 2 1) 5 2 1 (c) lim x 0 2 f ( x ) 5 lim x 0 2 } 1 x } 5 2‘ (d) lim x 0 1 f ( x ) 5 lim x 0 1 ( 2 1) 5 2 1 48. (a) lim x 2‘ f ( x ) 5 lim x 2‘ } x x 2 2 2 1 } 5 lim x 2‘ } x x } 5 1 (b) lim x f ( x ) 5 lim x } x 1 2 } 5 0 (c) lim x 0 2 f ( x ) 5 lim x 0 2 } x x 2 2 2 1 } 5 } 0 0 2 2 2 1 } 5 2 (d) lim x 0 1 f ( x ) 5 lim x 0 1 } x 1 2 } 5 ‘ 49. One possible answer: 50. One possible answer: 51. Note that } g f 1 1 ( ( x x ) ) / / f g 2 2 ( ( x x ) ) } 5 } f g 1 1 ( ( x x ) ) g f 2 2 ( ( x x ) ) } 5 } f f 1 2 ( ( x x ) ) / / g g 1 2 ( ( x x ) ) } . As x becomes large, } g f 1 1 } and } g f 2 2 } both approach 1. Therefore, using the above equation, } g f 1 1 / / f g 2 2 } must also approach 1. 52. Yes. The limit of ( f 1 g ) will be the same as the limit of g . This is because adding numbers that are very close to a given real number L will not have a significant effect on the value of ( f 1 g ) since the values of g are becoming arbitrarily large.
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