(Section 2.3: Limits and Infinity I) 2.3.26 Example 20Dominant 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 limx±²x³x2+x(). The answer is ±12, not 0. DTS can’t be used here, because neither term (neither xnor ±x2+x) is dominant; they are both “on the order of” x. A correct solution follows:
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