CalcNotes0203-page26 - (Section 2.3 Limits and Infinity I...

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(Section 2.3: Limits and Infinity I) 2.3.26 Example 20 Dominant Term Substitution (DTS) can be easily abused. We can use DTS if, at EVERY step in our solution, there is a clearly dominant term in the expression you’re finding the limit of (or, if analyzing a fraction, if there is a clearly dominant term in the numerator and a clearly dominant term in the denominator). For example, let’s say we want lim x ±² x ³ x 2 + x () . The answer is ± 1 2 , not 0. DTS can’t be used here, because neither term (neither x nor ± x 2 + x ) is dominant; they are both “on the order of” x . A correct solution follows:
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