CalcNotes0203-page10

# CalcNotes0203-page10 - ± 1 5 ² all yield 0(or ± as a...

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(Section 2.3: Limits and Infinity I) 2.3.10 The Rescaling Property of Some Limit Forms This property applies to Limit Forms that do not yield a limit that is a real nonzero constant; that is, the property applies to Limit Forms that yield: 0, ± , or ±² (or, for that matter, “DNE”). If such a Limit Form is rescaled by multiplying it by a positive real constant, then the resulting Limit Form will yield the same limit as the original. For example, the Limit Form 1 ± yields 0 (or, more precisely, 0 + ) as a limit, so the Limit Forms 2 ± , 3 ± , and 1/5 ± all yield 0 (or 0 + ) as a limit, also. Likewise, the Limit Form ± 1 ² yields 0 (or, more precisely, 0 ± ) as a limit, so the Limit Forms ± 2 ² , ± 3 ² , and
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Unformatted text preview: ± 1 / 5 ² all yield 0 (or ± ) as a limit, also. The Rescaling Property does not apply to Limit Forms that yield a limit that is a real nonzero constant. For example, the Limit Form 1 1 yields 1, but the Limit Form 2 1 yields 2. We will discuss similar Limit Form properties in a later section. Limit Form 1 ±² ( ) ³ ² . As a consequence, by our rules for signs and rescaling, we can also write: Limit Form c ±² ( ) ³ ² for any positive real constant c . Limit Form c ± ² ³ ( ) ( ) ´ ² ³ for any positive real constant c . Limit Form c ±² ( ) ³ ´ ² for any negative real constant c . Limit Form c ± ² ³ ( ) ( ) ´ ³ for any negative real constant c ....
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