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CalcNotes0201-page18

# CalcNotes0201-page18 - (Section 2.1 An Introduction to...

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(Section 2.1: An Introduction to Limits) 2.1.17 lim x ± 1 ² fx () = lim x ± 1 ² 2 x 2 = 21 2 = 2 The left-hand limit as x ± 1 ² : The relevant function rule is 2 x 2 , because that rule applies to the x -values in an open interval of the form c ,1 , where c < 1 ; for example, consider the interval 0.9,1 . lim x ± 1 + = lim x ± 1 + 2 x = = 2 The right-hand limit as x ± 1 + : The relevant function rule is 2 x , because that rule applies to the x -values in an open interval of the form 1, c , where c > 1 ; for example, consider the interval 1, 1.1 . lim x ± 1 = 2 The two-sided limit as x ± 1 : The left-hand and right-hand limits as x ± 1 exist and are equal, so the two-sided limit exists and equals their common value. lim x ± 0 ² = lim x ± 0 ² 3 = 3 The left-hand limit as x ± 0 ² : The relevant function rule is 3, because
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