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CalcNotes0205-page7 - (Section 2.5 The Indeterminate Forms...

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(Section 2.5: The Indeterminate Forms 0/0 and ± / ± ) 2.5.7 Example 2 (Rationalizing a Numerator or Denominator) Evaluate: lim x ± 0 9 ² x ² 3 x . Solution Method We will rationalize the numerator by multiplying the numerator and the denominator by the conjugate of the numerator; we are really multiplying by 1 in an effective way. The algebraic rule A ± B () A + B = A 2 ± B 2 allows us to eliminate the radicals in the numerator. Note : 9 ± x is defined as a real quantity on an open interval containing 0. Therefore, it is possible for the two-sided limit to exist, and the conjugate of the numerator is also appropriate to use.
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