(Section 2.5: The Indeterminate Forms 0/0 and ±/±) 2.5.7 Example 2 (Rationalizing a Numerator or Denominator)Evaluate: limx±09²x²3x. Solution MethodWe 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=A2±B2allows us to eliminate the radicals in the numerator. Note: 9±xis 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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lim, Limit of a function, Indeterminate form, Defined and undefined